a robust observer for discrete time nonlinear systems abstract this paper extends the results developed in ciccarella et al 1993 and presents a robust observer for discrete time nonlinear systems a simple robust and easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems combined parameter and state estimation is made for a numerical example which compares the robust observer to the observer given in ciccarella et al 1993

topology identification of weighted complex dynamical networks abstract recently various papers investigated the geometry features synchronization and control of complex network provided with certain topology while the exact topology of a network is sometimes unknown or uncertain using lyapunov theory we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model by receiving the network nodes evolution the topology of such kind of network with identical or different nodes or even with switching topology can be monitored experiments show that the methods presented in this paper are of high accuracy with good performance

chaos synchronization of different chaotic systems subjected to input nonlinearity abstract in this paper a unified mathematical expression describing a class of synchronization systems is presented for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied based on lyapunov stability theory a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the lyapunov sense in spite of the input nonlinearity this technique is applied to achieve chaos synchronization of three pairs of different chaotic systems lorenz chen chen liu and liu lorenz in drive response structure the numerical simulation results demonstrate the validity and feasibility of the proposed controller

estimating source location using normalized magnetic source strength calculated from magnetic gradient tensor data abstractfor a number of widely used models normalized source strength nss can be derived from eigenvalues of the magnetic gradient tensor the nss is proportional to a constant q normalized by the nth power of the distance between observation and integration points where q is a shape factor depending upon geometry of the model and n is the structural index the nss is independent of magnetization direction and its amplitude is only affected by the magnitude of magnetization the nss is also a homogenous function and satisfies euler s homogeneity equation therefore euler deconvolution of the nss can be used to estimate source location in our algorithm we use data points enclosed by a square window centered at maxima of the nss for simultaneously estimating the source location and structural index the window size is increased until it exceeds a predefined limit then the most reliable solution is chosen based on some statistical analysis minimum uncertainty one of the advantages of the presented

adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems we introduce a numerical approximation method for estimating an unknown parameter of a primary chaotic system which is partially observed through a scalar time series specifically we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed secondary system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter the salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted we present numerical examples for the lorenz system which show how our algorithm can be considerably faster than some previously proposed methods

synchronization based topology identification of weighted general complex dynamical networks with time varying coupling delay abstract many existing papers investigated the geometric features control and synchronization of complex dynamical networks provided with certain topology however the exact topology of a network is sometimes unknown or uncertain based on lasalle s invariance principle we propose an adaptive feedback technique to identify the exact topology of a weighted general complex dynamical network model with time varying coupling delay by receiving the network nodes evolution the topology of such a kind of network with identical or different nodes or even with varying topology can be monitored in comparison with previous methods time delay is taken into account in this simple analytical and systematic synchronization based technique particularly the weight configuration matrix is not necessarily symmetric or irreducible and the inner coupling matrix need not be symmetric illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme

the synchronization of complex dynamical networks with similar nodes and coupling time delay the synchronization for a class of complex dynamical network with similar nodes and coupling time delay is investigated the dimensions of the dynamical nodes in the complex network are different moreover the coupling time delays of the dynamical nodes are also different and the decentralized control strategies are designed in term of the information of the similar parameters in dynamical complex networks by using the method of linear matrix inequality the definition of the synchronization manifold is constructed and the time delay independent criterion of the synchronization of the complex dynamical networks is derived finally a numerical example is presented to demonstrate the application of the theoretical results

bilinear integral operators with certain hypersingularities abstract in this paper we establish the sharp l p boundedness for the bilinear integral operators with certain hypersingularities that generalize the bilinear hilbert transform

modeling and nonlinear parameter estimation with kronecker product representation for coupled oscillators and spatiotemporal systems we focus here on the question of global modeling that is building an ordinary differential equation ode of minimal dimensions which models a given multivariate time dependent data set we give proof of convergence of the given method we will furthermore introduce a new method which adapts the least squares best approximation by a kronecker product representation c f van loan n pitsianis approximation with kronecker products www math tkk fi mhuhtane kronecker ps to analyze underlying structure when it exists as a system of coupled oscillators several examples are presented including diffusively coupled chaotic systems some interesting prospective problems will be briefly discussed in the conclusions

use of synchronization and adaptive control in parameter estimation from a time series a technique is introduced for estimating unknown parameters when a time series of only one variable from a multivariate nonlinear dynamical system is given the technique employs a combination of two different control methods linear feedback for synchronizing system variables and adaptive control and is based on dynamic minimization of synchronization error the technique is shown to work even when the unknown parameters appear in the evolution equations of the variables other than the one for which the time series is given the technique not only establishes that explicit detailed information about all system variables and parameters is contained in a scalar time series but also gives a way to extract it out under suitable conditions illustrations are presented for lorenz and rossler systems and a nonlinear dynamical system in plasma physics also it is found that the technique is reasonably stable against noise in the given time series and the estimated value of a parameter fluctuates around the correct value with the error of estimation growing linearly with the noise strength for small noise

on the application of euler deconvolution to the analytic signal standard euler deconvolution is applied to potential field functions that are homogeneous and harmonic homogeneity is necessary to satisfy the euler deconvolution equation itself whereas harmonicity is required to compute the vertical derivative from data collected on a horizontal plane according to potential field theory the analytic signal modulus of a potential field is a homogeneous function but is not a harmonic function hence the vertical derivative of the analytic signal is incorrect when computed by the usual techniques for harmonic functions and so also is the consequent euler deconvolution we show that the resulting errors primarily affect the structural index and that the estimated values are always notably lower than the correct ones the consequences of this error in the structural index are equally important whether the structural index is given as input as in standard euler deconvolution or represents an unknown to be solved for the analysis of a case history confirms serious errors in the estimation of structural index if the vertical derivative of the analytic signal is computed as for harmonic functions we suggest computing the first vertical derivative of the analytic signal modulus taking into account its nonharmonicity by using a simple finite difference algorithm when the vertical derivative of the analytic signal is computed by finite differences the depth to source and the structural index consistent with known source parameters are in fact obtained

parameter identification of dynamical systems from time series in this paper synchronization based parameter identification of dynamical systems from time series is carefully revisited it is shown based on rigorous theoretical analysis and concrete counterexamples that some recent research reports on this issue are incomplete or even incorrect a linear independence condition is pointed out which is sufficient for such parameter identification of general dynamical systems

parameter estimation of delay dynamical system from a scalar time series under external noise we introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series sufficient condition for synchronization is derived using krasovskii lyapunov theory this scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations one of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available we present numerical examples for mackey glass system with periodic delay time which are used to illustrate the validity of this scheme the corresponding numerical results and the effect of external noise are also studied

adachi like chaotic neural networks requiring linear time computations by enforcing a tree shaped topology the adachi neural network adnn is a fascinating neural network nn which has been shown to possess chaotic properties and to also demonstrate associative memory am and pattern recognition pr characteristics variants of the adnn have also been used to obtain other pr phenomena and even blurring an unsurmountable problem associated with the adnn and the variants referred to above is that all of them require a quadratic number of computations this is essentially because the nns in each case are completely connected graphs in this paper we consider how the computations can be significantly reduced by merely using a linear number of computations to achieves this we extract from the original completely connected graph one of its spanning trees we then address the problem of computing the weights for this spanning tree this is done in such a manner that the modified tree based nn has approximately the same input output characteristics and thus the new weights are themselves calculated using a gradient based algorithm by a detailed experimental analysis we show that the new linear time adnn like network possesses chaotic and pr properties for different settings as far as we know such a tree based adnn has not been reported and the results given here are novel

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

identification of delays and discontinuity points of unknown systems by using synchronization of chaos in this paper we present an approach in which synchronization of chaos is used to address identification problems in particular we are able to identify i the discontinuity points of systems described by piecewise dynamical equations and ii the delays of systems described by delay differential equations delays and discontinuities are widespread features of the dynamics of both natural and manmade systems the foremost goal of the paper is to present a general and flexible methodology that can be used in a broad variety of identification problems

darboux transformation of the variable coefficient nonlocal equation abstract in this paper we investigate an integrable variable coefficient nonlocal nonlinear schrodinger equation nnls for the first time with the help of lax pair darboux transformations and exact solutions to the variable coefficient nnls are studied it is shown that we can get many more general solutions than equation with constant coefficient in addition some solutions of variable coefficient nnls equation with specific coefficients are given

stabilization of delay systems delay dependent impulsive control the stabilization problem of delay systems is studied under the delay dependent impulsive control the main contributions of this technical note are that for one thing it shows that time delays in impulse term may contribute to the stabilization of delay systems that is a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks for another it shows the robustness of impulsive control that is the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization in this technical note from impulsive control point of view we firstly propose an impulsive delay inequality then we apply it to the delay systems which may be originally unstable and derive some delay dependent impulsive control criteria to ensure the stabilization of the addressed systems the effectiveness of the proposed strategy is evidenced by two illustrative examples

darboux transformation and rogue wave solutions for the variable coefficients coupled hirota equations abstract we construct the lax pair and darboux transformation for the variable coefficients coupled hirota equations based on modulation instability and by taking the limit approach we derive two types of nth order rogue wave solutions with different dynamic structures in compact determinant representations the explicit first order rogue wave solution is presented prolific vector rogue wave patterns such as the dark bright composite three sister quadruple and sextuple rogue waves with multiple compression points are demonstrated in particular in contrast to the standard peregrine combs unusual vector rogue wave combs such as the dark bright and composite rogue wave combs are revealed by choosing sufficiently large periodic modulation amplitudes further some wave characteristics such as the difference between light intensity and continuous wave background and pulse energy evolution of the dark rogue wave solution that features multiple compression points are discussed in detail

estimating model parameters by chaos synchronization using chaos synchronization and a proposed iterative method of parameter adaptation we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters this parameter adaptation method can be applied to a spatiotemporal chaotic system with a one way coupled map lattice as a biomedical application this method is capable of estimating the asymmetric tension parameter of a vocal fold model

pragmatical adaptive synchronization new fuzzy model of two different and complex chaotic systems by new adaptive control abstract in this paper 1 a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and 2 a new adaptive approach and a new control lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors by using this new model the numbers of fuzzy rules of chaotic systems can be reduced from 2 n to 2 n and only 2 subsystems are needed where n is the number of nonlinear terms the fuzzy systems become much simpler in addition through the new fuzzy model the new fuzzy systems are much simpler than t s fuzzy systems when nonlinear systems are complicated and can be used to any other kind of application in fuzzy logic control or fuzzy modeling mathieu van der pol system which is called m v system in this paper and quantum cellular neural networks nanosystem which is called q cnn system in this paper are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control lyapunov function the t s fuzzy modeling and traditional adaptive control are also given in appendix b t s fuzzy model of chaotic systems appendix c traditional adaptive method for comparison

parameter evaluation from time sequences using chaos synchronization unknown parameters in nonlinear equations are estimated from chaotic time sequences using chaos synchronization the method is based on a random optimization method the parameters are randomly searched for in a sequential manner as the degree of the chaos synchronization is increased the method is applied for the parameter evaluation in the lorenz equation and the lang kobayashi model for the chaotic semiconductor laser

dual synchronization of chaos in colpitts electronic oscillators and its applications for communications we demonstrate the dual synchronization of chaos in two pairs of one way coupled colpitts electronic oscillators by both experiment and numerical simulation we use the cross coupling method where the difference in voltage between the sum of two master oscillators and one slave oscillator is injected into the other slave oscillator as an electrical current for dual synchronization of chaos we have investigated the regions for achieving dual synchronization of chaos when one of the internal parameters is mismatched between the master and slave oscillators we numerically obtain a similar curve for the accuracy of synchronization to that obtained from our experiments a communication scheme using dual synchronization of chaos is also proposed and demonstrated

single shooting homotopy method for parameter identification in dynamical systems an algorithm for identifying parameters in dynamical systems is developed in this work using homotopy transformations and the single shooting method the equations governing the dynamics of the mathematical model are augmented with observer like homotopy terms that smooth the objective function as a result premature convergence to a local minimum is avoided and the obtained parameter estimates are globally optimal numerical examples are presented to demonstrate the application of the proposed approach to chaotic systems

a special full state hybrid projective synchronization in symmetrical chaotic systems a special full state hybrid projective synchronization type is proposed in this paper the anti synchronization and complete synchronization can be achieved simultaneously in this new synchronization phenomenon we point out how to realize this synchronization in chaotic systems anti synchronization in symmetrical coordinate subspace and complete synchronization in its normal coordinate subspace two illustrative examples multi scroll chaotic system by the partial lyapunov stability theory and a four dimensional chaotic system by the invariance principle of differential equation are presented to exhibit this new synchronization

closed form formula of magnetic gradient tensor for a homogeneous polyhedral magnetic target a tetrahedral grid example abstracta closed form formula is developed for the full magnetic gradient tensor of a polyhedral body with a homogeneous magnetization vector it is based on the direct derivative technique on the closed form of the magnetic field these analytical expressions are implemented into an easy to use c package which simultaneously calculates the magnetic potential the magnetic field and the full magnetic gradient tensor for magnetic targets modern unstructured tetrahedral grids are adopted to represent the polyhedral body so that our code can deal with arbitrarily complicated magnetic targets a prismatic body is tested to verify the accuracies of our closed form formula excellent agreements are obtained between our closed form solutions and solutions of a prismatic magnetic body with differences up to machine precision a pipeline model is used to demonstrate its capability to deal with complicated magnetic targets this c code is freely available to the magnetic exploration community

tensor deconvolution a method to locate equivalent sources from full tensor gravity data we present a method dedicated to the interpretation of full tensor gravity gradiometry ftg data called tensor deconvolution it is especially designed to benefit from the simultaneous use of all the ftg components and of the gravity field in particular it uses tensor scalar invariants as a basis for source location the invariant expressions involve all of the independent components of the tensor this method is a tensor analog of euler deconvolution but has the following advantages compared to the conventional euler deconvolution method 1 it provides a solution at every observation point without the use of a sliding window 2 it determines the structural index automatically as a consequence the structural index follows the variations of the field morphology 3 it uses all components of the measured full gradient tensor and gravity field thus reducing errors caused by random noise it is based on scalar invariants that are by nature insensitive to the orientation of the measuring device we tested our method on both noise free and noise contaminated data these tests show that tensor solutions cluster in the vicinity of the center of causative bodies whereas euler solutions better outline their edges hence these methods should be combined for improved contouring and depth estimation in addition we use a clustering method to improve the selection of solutions which proves advantageous when data are noisy or when signals from close causative bodies interfere introduction

statistical methods of parameter estimation for deterministically chaotic time series we discuss the possibility of applying some standard statistical methods the least square method the maximum likelihood method and the method of statistical moments for estimation of parameters to deterministically chaotic low dimensional dynamic system the logistic map containing an observational noise a segmentation fitting maximum likelihood ml method is suggested to estimate the structural parameter of the logistic map along with the initial value x 1 considered as an additional unknown parameter the segmentation fitting method called piece wise ml is similar in spirit but simpler and has smaller bias than the multiple shooting previously proposed comparisons with different previously proposed techniques on simulated numerical examples give favorable results at least for the investigated combinations of sample size n and noise level besides unlike some suggested techniques our method does not require the a priori knowledge of the noise variance we also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed bayesian approaches we note the trade off between the need of using a large number of data points in the ml analysis to decrease the bias to guarantee consistency of the estimation and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition the method of statistical moments for the estimation of the parameter of the logistic map is discussed this method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically not only numerically

the function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems the function cascade synchronization scheme for the hyperchaotic systems is proposed to make the states of two identical the hyperchaotic systems both with and without uncertain parameters asymptotically synchronized based on lyapunov stability theory and the proposed scheme the lu system and chen hyperchaotic system with and without uncertain parameters are chosen to achieve the function cascade synchronization simultaneously numerical simulations are used to verify the effectiveness and feasibility of the presented control scheme

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

observers for discrete time nonlinear systems abstract the problem of observers for discrete time nonlinear systems has been considered and a simple easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems some numerical examples show the effectiveness of the proposed observer

toward a three dimensional automatic interpretation of potential field data via generalized hilbert transforms fundamental relations the paper extends to three dimensions 3 d the two dimensional 2 d hilbert transform relations between potential field components for the 3 d case it is shown that the hilbert transform is composed of two parts with one part acting on the x component and one part on the y component as for the previously developed 2 d case it is shown that in 3 d the vertical and horizontal derivatives are the hilbert transforms of each other the 2 d cauchy riemann relations between a potential function and its hilbert transform are generalized for the 3 d case finally the previously developed concept of analytic signal in 2 d can be extended to 3 d as a first step toward the development of an automatic interpretation technique for potential field data

realization of parameters identification in only locally lipschitzian dynamical systems with multiple types of time delays most of the existing results for identifying parameters in dynamical systems through adaptive coupling techniques always require a uniform lipschitz condition on system vector fields however it is not this requirement but the only locally lipschitz condition that is more suitable for many nonlinear systems in real applications also time delays sometimes are essential for modeling real systems so that in addition to the discrete form time delays in the distributed form could be considered this paper thus considers the problem of parameters identification in only locally lipschitzian dynamical systems with multiple types of time delays through adaptive coupling techniques in particular the paper proposes some linear independence conditions for realization of parameters identification in both nonautonomous and autonomous systems and draws a comparison between these conditions and the persistent of excitation condition which is used frequently in the literature moreover the paper proposes an index t

nonlocal symmetry darboux transformation and soliton cnoidal wave interaction solution for the shallow water wave equation abstract in classical shallow water wave sww theory there exist two integrable one dimensional sww equation hirota satsuma hs type and ablowitz kaup newell segur akns type in the boussinesq approximation in this paper we mainly focus on the integrable sww equation of akns type the nonlocal symmetry in form of square spectral function is derived starting from its lax pair infinitely many nonlocal symmetries are presented by introducing the arbitrary spectrum parameter these nonlocal symmetries can be localized and the sww equation is extended to enlarged system with auxiliary dependent variables then darboux transformation for the prolonged system is found by solving the initial value problem similarity reductions related to the nonlocal symmetry and explicit group invariant solutions are obtained it is shown that the soliton cnoidal wave interaction solution which represents soliton lying on a cnoidal periodic wave background can be obtained analytically interesting characteristics of the interaction solution between soliton and cnoidal periodic wave are displayed graphically

generalized synchronization of chaotic systems by pure error dynamics and elaborate lyapunov function abstract the generalized synchronization is studied by applying pure error dynamics and elaborate lyapunov function in this paper generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation instead of current mixed error dynamics in which master state variables and slave state variables are presented the elaborate lyapunov function is applied rather than the current plain square sum lyapunov function deeply weakening the power of lyapunov direct method the scheme is successfully applied to both autonomous and nonautonomous double mathieu systems with numerical simulations

impulsive control of lorenz system abstract in this paper an impulsive control scheme of the lorenz system is presented first we use the theory of impulsive differential equation to find conditions under which impulsively controlled lorenz system is asymptotically stable then we give the estimate of the upper bound of impulse interval for asymptotically stable control numerical experimental results are presented

integral representation of product factorable bilinear operators and summability of bilinear maps on c k spaces abstract we present a constructive technique to represent classes of bilinear operators that allow a factorization through a bilinear product providing a general version of the well known characterization of integral bilinear forms as elements of the dual of an injective tensor product we show that this general method fits with several known situations coming from different contexts harmonic analysis c algebras c k spaces operator theory polynomials providing a unified approach to the integral representation of a broad class of bilinear operators some examples and applications are also shown regarding for example operator spaces and summability properties of bilinear maps

adaptive exponential synchronization of delayed chaotic networks abstract this paper deals with the global exponential synchronization of a class of delayed chaotic networks under some simple conditions the global synchronization of a network about its all variables is derived by only considering the global synchronization of its partial variables furthermore based on the halanay inequality technique some delay independent criteria are obtained to ensure the adaptive exponential synchronization of the model and the simpler less conservative and more efficient results are easy to be verified in engineering applications finally an illustrative example is given to demonstrate the effectiveness of the presented synchronization scheme

lyapunov exponents from observed time series we examine the question of accurately determining lyapunov exponents for a time series we find that it is advantageous to use local mappings with higher order taylor series rather than linear maps as done earlier we demonstrate this procedure for the ikeda map and the lorenz system we present methods for identifying spurious exponents by analyzing data set singularities and by determining the lyapunov direction vectors the behavior of spurious exponents in the presence of noise is also investigated and found to be different from that of the true exponents

estimating parameters of a nonlinear dynamical system a method based on a modified newton raphson scheme is presented to estimate parameters of a nonlinear dynamical system from the time series data of the variables the method removes some of the problems associated with the standard synchronization based methods an important achievement of this method is that it is possible to determine the exact form of dynamical equations for systems with quadratic nonlinearity

estimation of parameters in nonlinear systems using balanced synchronization using synchronization between observations and a model with undetermined parameters is a natural way to complete the specification of the model the quality of the synchronization a cost function to be minimized typically is evaluated by a least squares difference between the data time series and the model time series if the coupling between the data and the model is too strong this cost function is small for any data and any model and the variation of the cost function with respect to the parameters of interest is too small to permit selection of an optimal value of the parameters we introduce two methods for balancing the competing desires of a small cost function for the quality of the synchronization and the numerical ability to determine parameters accurately one method of balanced synchronization adds to the synchronization cost function a requirement that the conditional lyapunov exponent of the model system conditioned on being driven by the data remain negative but small in magnitude the other method allows the coupling between the data and the model to vary in time according to the error in synchronization this method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined examples are explored which have deterministic chaos with and without noise in the data signal

collapse of ordered spatial pattern in neuronal network abstract spatiotemporal systems can emerge some regular spatial patterns due to self organization or under external periodical pacing while external attack or intrinsic collapse can destroy the regularity in the spatial system for an example the electrical activities of neurons in nervous system show regular spatial distribution under appropriate coupling and connection it is believed that distinct regularity could be induced in the media by appropriate forcing or feedback while a diffusive collapse induced by continuous destruction can cause breakdown of the media in this paper the collapse of ordered spatial distribution is investigated in a regular network of neurons morris lecar hindmarsh rose in two dimensional array a stable target wave is developed regular spatial distribution emerges by imposing appropriate external forcing with diversity or generating heterogeneity parameter diversity in space the diffusive invasion could be produced by continuous parameter collapse or switch in local area e g the diffusive poisoning in ion channels of potassium in morris lecar neurons causes breakdown in conductance of channels it is found that target wave dominated regularity can be suppressed when the collapsed area is diffused in random statistical correlation functions for sampled nodes neurons are defined to detect the collapse of ordered state by series analysis

master slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control global chaos synchronization of two identical non autonomous horizontal platform systems coupled by linear state error feedback controller is investigated the sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time varied systems and lyapunov s direct method of which the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices in the examples the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified it is analytically and numerically examined that the synchronization criteria based on lyapunov s direct method are sharper than the criteria based on the stability theory of linear time varied systems

chaos synchronization and parameter estimation from a scalar output signal we propose an observer based approach for chaos synchronization and parameter estimation from a scalar output signal to begin with we use geometric control to transform the master system into a standard form with zero dynamics then we construct a slaver to synchronize with the master using a combination of slide mode control and linear feedback control within a finite time partial synchronization is realized which further results in complete synchronization as time tends to infinity even if there exists model uncertainty in the slaver we can also estimate the unknown model parameter by a simple adaptive rule

system identification for the ott grebogi yorke controller design a technique to compute the linearized poincar e map and the sensitivity vector required for the implementation of an ott grebogi yorke ogy controller from experimental data is presented unlike previous methods the linearized map and the sensitivity vector are computed using only data collected over a single period of the limit cycle the main advantage of the present method is the fact that it eliminates the long waiting period required to design an ogy controller using previously known methods numerical examples are presented using the duffing oscillator with random perturbations to simulate noisy experimental data

stochastic parameter estimation in nonlinear time delayed vibratory systems with distributed delay abstract the stochastic estimation of parameters and states in linear and nonlinear time delayed vibratory systems with distributed delay is explored the approach consists of first employing a continuous time approximation to approximate the delayed integro differential system with a large set of ordinary differential equations having stochastic excitations then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique by adapting the extended kalman bucy filter to the augmented filtering problem the unknown parameters of the time delayed system are estimated from noise corrupted possibly incomplete measurements of the states similarly the upper bound of the distributed delay can also be estimated by the proposed technique as an illustrative example to a practical problem in vibrations the parameter delay upper bound and state estimation from noise corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated

simple adaptive feedback controller for identical chaos synchronization based on the invariance principle of differential equations a simple adaptive feedback scheme is proposed to strictly synchronize almost all chaotic systems unlike the usual linear feedback the variable feedback strength is automatically adapted to completely synchronize two almost arbitrary identical chaotic systems so this scheme is analytical and simple to implement in practice moreover it is quite robust against the effect of noise the famous lorenz and rossler hyperchaos systems are used as illustrative examples

synchronization of neural networks based on parameter identification and via output or state coupling for neural networks with all the parameters unknown we focus on the global robust synchronization between two coupled neural networks with time varying delay that are linearly and unidirectionally coupled first we use lyapunov functionals to establish general theoretical conditions for designing the coupling matrix neither symmetry nor negative positive definiteness of the coupling matrix are required under less restrictive conditions the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states second by employing the invariance principle of functional differential equations a simple analytical and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time varying delay based on the parameter identification of uncertain delayed neural networks finally numerical simulations validate the effectiveness and feasibility of the proposed technique

seeker optimization algorithm for parameter estimation of time delay chaotic systems time delay chaotic systems have some very interesting properties and their parameter estimation has received increasing interest in the recent years it is well known that parameter estimation of a chaotic system is a nonlinear multivariable and multimodal optimization problem for which global optimization techniques are required in order to avoid local minima in this work a seeker optimization algorithm soa based method is proposed to address this issue in the soa search direction is based on the empirical gradients by evaluating the response to the position changes and step length is based on uncertainty reasoning by using a simple fuzzy rule the performance of the algorithm is evaluated on two typical test systems moreover two state of the art algorithms i e particle swarm optimization and differential evolution are also considered for comparison the simulation results show that the proposed algorithm is better than or at least as good as the other two algorithms and can effectively solve the parameter estimation problem of time delay chaotic systems

driving and synchronizing by chaotic impulses for a class of dynamical systems driven by chaotic impulses we give conditions for the occurrence of chaos locking it is shown how the concept of time discontinuous coupling of two chaotic systems may lead to generalized synchronization the method of synchronization is interpreted as a nonlinear analog of the sampling theorem furthermore we examine the effect of amplitude quantization of the driving signal on their synchronization even though two time discontinuously coupled dynamical systems are no more exactly synchronized when the driving signal is digitized their trajectories are close enough to allow correct transmission of digital information signals between them textcopyright 1996 the american physical society

synchronization of chaotic orbits the effect of a finite time step two chaotic orbits can be synchronized by driving one of them by the other some of the variables of the driven orbit are set continuously to the corresponding variables of the drive orbit it has been seen that synchronization can be achieved if the subsystem lyapunov exponents corresponding to the remaining or response variables are all negative we find that a procedure where the drive variable is set at discrete times can also achieve synchronization however the synchronization criterion is altered by the effect of the drive being set at finite time steps an important consequence of this is found in the lorenz system where synchronization can be achieved with z as the drive variable despite the existence of a marginal subsystem lyapunov exponent we also find that synchronization can be achieved for the rossler attractor with z as the drive even though the largest subsystem lyapunov exponent is positive in addition we find that there is an optimal time step corresponding to the fastest rate of convergence for both cases above our synchronization criterion reduces to the usual subsystem lyapunov exponent criterion in the limit of the time step tending to zero

slower speed and stronger coupling adaptive mechanisms of chaos synchronization we show that two initially weakly coupled chaotic systems can achieve synchronization by adaptively reducing their speed and or enhancing the coupling strength explicit adaptive algorithms for speed reduction and coupling enhancement are provided we apply these algorithms to the synchronization of two coupled lorenz systems it is found that after a long time adaptive process the two coupled chaotic systems can achieve synchronization with almost the minimum required coupling speed ratio

understanding 3d analytic signal amplitude the concept of the analytic signal goes back at least to ville 1948 the analytic signal a x of function f x is a complex quantity defined as where h f x represents the hilbert transform of f x nabighian 1972 1974 applies the analytic signal concept to potential field data in two dimensions for a potential field x measured along the x axis at a constant observation height z and generated by a 2d source aligned parallel to the y axis the horizontal derivative x and the vertical derivative z are a hilbert transform pair

soliton solutions of an integrable nonlocal modified korteweg de vries equation through inverse scattering transform abstract it is well known that the nonlinear schrodinger nls equation is a very important integrable equation ablowitz and musslimani introduced and investigated an integrable nonlocal nls equation through inverse scattering transform very recently we proposed an integrable nonlocal modified korteweg de vries equation mkdv which can also be found in the papers of ablowitz and musslimani we have constructed the darboux transformation and soliton solutions for the nonlocal mkdv equation in this paper we will investigate further the nonlocal mkdv equation we will give its exact solutions including soliton and breather through inverse scattering transformation these solutions have some new properties which are different from the ones of the mkdv equation

parameter adaptive identical synchronization disclosing lorenz chaotic masking a parameter adaptive rule that globally synchronizes oscillatory lorenz chaotic systems with initially different parameter values is reported in principle the adaptive rule requires access to the three state variables of the drive system but it has been readapted to work with the exclusive knowledge of only one variable a potential message carrier the rule is very robust and can be used to trace parameter modulation conveying hidden messages the driven system is defined according to a drive driven type of coupling that guarantees synchronization if parameters are identical from any arbitrary initial state the parameters of the driven system are dynamically adapted to reach convergence to the drive parameter values at this point synchronization mismatch or parameter tracing is used to unmask any potential hidden message

pragmatical adaptive chaos control from a new double van der pol system to a new double duffing system a new pragmatical adaptive control method for different chaotic systems is proposed traditional chaos control is limited to decrease chaos of one chaotic system this method enlarges the effective scope of chaos control we can control a chaotic system e g a new chaotic double van der pol system to a given chaotic or regular system e g a new chaotic double duffing system or to a damped simple harmonic system by a pragmatical theorem of asymptotical stability based on an assumption of equal probability of initial point an adaptive control law is derived such that it can be proved strictly that the common zero solution of error dynamics and of parameter dynamics is asymptotically stable numerical simulations are given to show the effectiveness of the proposed scheme

synchronization based approach for estimating all model parameters of chaotic systems the problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved the variational calculus based method is robust in the presence of noise enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system the method is demonstrated using the lorenz rossler chaos and hyperchaos models its possible application in decoding communications using chaos is discussed

exponential rm h _ infty synchronization of general discrete time chaotic neural networks with or without time delays this brief studies exponential h synchronization of a class of general discrete time chaotic neural networks with external disturbance on the basis of the drive response concept and h control theory and using lyapunov krasovskii or lyapunov functional state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays but also reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities most discrete time chaotic systems with or without time delays such as hopfield neural networks cellular neural networks bidirectional associative memory networks recurrent multilayer perceptrons cohen grossberg neural networks chua s circuits etc can be transformed into this general chaotic neural network to be h synchronization controller designed in a unified way finally some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods

inferring local dynamics and connectivity of spatially extended systems with long range links based on steady state stabilization a method is presented for system identification of spatially extended systems with structural inhomogeneities of local dynamics and additional long range links the proposed identification procedure is based on steady state stabilization and is illustrated with an inhomogeneous two dimensional grid of coupled fitzhugh nagumo models

exponential synchronization of chaotic systems subject to uncertainties in the control input a sliding mode control technique is introduced for exponential synchronization of chaotic systems these systems are described by a general form including matched and unmatched nonlinear functions a new hitting free switching surface of proportional integral type is proposed this type of switching surface is without the hitting process if the attraction of sliding manifold is ensured this property makes it easy to exponentially synchronize the master slave chaotic systems based on this switching surface a robust sliding mode controller smc is derived to guarantee the attraction of sliding manifold even when the system is subjected to input uncertainties an example is included to illustrate the results developed in this paper

magnetic interpretation in three dimensions using euler deconvolution magnetic survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using euler s homogeneity relation the method employs gradients either measured or calculated data need not be pole reduced so that remanence is not an interfering factor geologic constraints are imposed by use of a structural index model studies show that the method can locate or outline confined sources vertical pipes dikes and contacts with remarkable accuracy a field example using data from an intensively studied area of onshore britain shows that the method works well on real data from structurally complex areas and provides a series of depth labeled euler trends which mark magnetic edges notably faults with good precision

parameter estimation in non extensive thermostatistics abstract equilibrium statistical physics is considered from the point of view of statistical estimation theory this involves the notions of statistical model of estimators and of exponential family a useful property of the latter is the existence of identities obtained by taking derivatives of the logarithm of the partition sum it is shown that these identities still exist for models belonging to generalised exponential families in which case they involve escort probability distributions the percolation model serves as an example a previously known identity is derived it relates the average number of sites belonging to the finite cluster at the origin the average number of perimeter sites and the derivative of the order parameter

chaos synchronization and parameter identification for gyroscope system synchronization of chaos for a two degree of freedom heavy symmetric gyroscope system are studied in this paper because of the nonlinear terms of the system the system exhibits both regular and chaotic motions by lyapunov stability theory with control terms by adaptive control and by random optimization method the synchronization of two identical systems and tracking of the parameter of the systems are studied

failure of parameter identification based on adaptive synchronization techniques in this paper several examples as well as their numerical simulations are provided to show some possible failures of parameter identification based on the so called adaptive synchronization techniques these failures might arise not only when the synchronized orbit produced by the driving system is designed to be either some kind of equilibrium or to be some kind of periodic orbit but also when this orbit is deliberately designed to be chaotic the reason for emergence of these failures is theoretically analyzed in the paper and the boundedness of all trajectories generated by the coupled systems is rigorously proved moreover synchronization techniques are proposed to realize complete synchronization and unknown parameter identification in a class of systems where nonlinear terms are not globally lipschitz in addition unknown parameter identification is studied in coupled systems with time delays

function projective synchronization in complex networks with switching topology and stochastic effects although function projective synchronization in complex dynamical networks has come into the limelight in recent years litter research has been published on the problem in the dynamical networks with switching topology and stochastic effects this study aims to fill the gap in this paper the problem of function projective synchronization is investigated for complex networks with switching topology and stochastic effects a hybrid feedback control method is designed to achieve function projective synchronization for the complex network using the property of martingale and gronwally inequality we obtain some conditions to guarantee that the complex network can realize mean square synchronization and mean square exponential synchronization respectively furthermore we also present a probability approach to the method of lyapunov functionals to analyze function projective synchronization in the dynamical network under a particular assumption our approaches not only can replace the lasalle type theorem but also allow improvements of existing results in the literature in particular the study also presents an equivalent way of regarding ito integral which may be a useful tool to deal with the problem of synchronization in variety of complex dynamical networks with stochastic effects finally some numerical examples are provided to demonstrate the effectiveness of the proposed approach

adaptive control in nonlinear dynamics abstract we extend an adaptive control algorithm recently suggested by huberman and lumer to multi parameter and higher dimensional nonlinear systems this control mechanism is remarkably effective in returning a system to its original dynamics after a sudden perturbation in the system parameters changes the dynamical behaviour we find that in all cases the recovery time is linearly proportional to the inverse of control stiffness for small stiffness in higher dimensions there is an additional optimization problem since increasing stiffness beyond a certain value can retard recovery the control of fixed point dynamics in systems capable of a wide variety of dynamical behaviour is demonstrated we further suggest methods by which periodic motion such as limit cycles can be adaptively controlled and demonstrate the robustness of the procedure in the presence of additive background noise

dynamic algorithm for parameter estimation and its applications we consider a dynamic method based on synchronization and adaptive control to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series we present an important extension of the method when the time series of a scalar function of the variables of the underlying dynamical system is given we find that it is possible to obtain synchronization as well as parameter estimation using such a time series we then consider a general quadratic flow in three dimensions and discuss the applicability of our method of parameter estimation in this case in practical situations one expects only a finite time series of a system variable to be known we show that the finite time series can be repeatedly used to estimate unknown parameters with an accuracy that improves and then saturates to a constant value with repeated use of the time series finally we suggest an important application of the parameter estimation method we propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system we show that our method produces exact synchronization with the given time series only when the trial function has a form identical to that of the perturbation

on a recursive method for the estimation of unknown parameters of partially observed chaotic systems we investigate a recently proposed method for on line parameter estimation and synchronization in chaotic systems this novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series it works by periodically updating the parameter of interest in a secondary system with the same functional form as the primary one but no explicit coupling between their dynamic variables in order to minimize a suitably defined cost function in this paper we review the basics of the method and investigate its robustness and new extensions in particular we study the performance of the novel technique in the presence of noise either observational i e an additive contamination of the observed time series or dynamical i e a random perturbation of the system dynamics and when there is a mismatch between the primary and secondary systems numerical results including comparisons with other techniques are presented finally we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations

synchronization based estimation of all parameters of chaotic systems from time series by a simple combination of adaptive scheme and linear feedback with the updated feedback strength for a large class of chaotic systems it is proved rigorously by using the invariance principle of differential equations that all unknown model parameters can be estimated dynamically this approach supplies a systematic and analytical procedure for estimating parameters from time series and it is simple to implement in practice in addition this method is quite robust against the effect of noise and able to respond rapidly to changes in operating parameters of the experimental system lorenz and r ossler hyperchaos systems are used to illustrate the validity of this technique

on general rogue waves in the parity time symmetric nonlinear schrodinger equation abstract this article addresses the question of general rogue wave solutions in the nonlocal parity time symmetric nonlinear schrodinger equation by generalizing the previous bilinear method large classes of rogue waves are derived as gram determinants with schur polynomial elements it is shown that these rogue waves contain previously reported ones as special cases more importantly they contain many new rogue wave families it is conjectured that the rogue waves derived in this article are all rogue wave solutions in the parity time symmetric nonlinear schrodinger equation

structure identification based on steady state control experimental results and applications we report experimental results on structure identification of nonlinear systems by a steady state control method the idea underlying the method is to drive the nonlinear system to steady state by applying a suitable feedback control input it turns out experimentally that this control based structure identification method can be used for some applications such as estimation of initial conditions and state variables of nonlinear systems and structure identification of some special elements two attractors of the chua oscillator are presented to illustrate the reliability of the suggested techniques under the hypotheses of measurable state variables and physical access to the system for implementing the proportional feedback

breather lump and x soliton solutions to nonlocal kp equation abstract breather lump and x soliton solutions are presented via the hirota bilinear method to the nonlocal 2 1 dimensional kp equation derived from the alice bob system the resulting breather contains two cases one is the line breather and another is the normal breather both of which are different from the solutions of the classical 2 1 dimensional kp equation the x soliton is found with the long wave limit by some constraints to the parameters the lump solution is obtained in virtue of two methods one is as the long wave limit of breather theoretically the other is with the quadratic function method which can be guaranteed rationally localized in all directions in the space under some constraints of the parameters by choosing specific values of the involved parameters the dynamic properties of some breather lump solutions to nonlocal kp equation are plotted as illustrative examples

parameter and state estimation of experimental chaotic systems using synchronization we examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems we focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic colpitts oscillator as an example system we explore the impact of model imperfection on the ability to extract valid information from an experimental system we compare two optimization methods an initial value method and a constrained method each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold we explore both time dependent and time independent coupling and discuss the use of periodic impulse coupling we also examine both optimized and fixed or manually adjusted coupling for the case of an optimized time dependent coupling function u t we find a robust structure which includes sharp peaks and intervals where it is zero this structure shows a strong correlation with the location in phase space and appears to depend on noise imperfections of the model and the lyapunov direction vectors for time independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength comparison of this result with that obtained using simulated data may provide one measure of model imperfection the constrained method with time dependent coupling appears to have benefits in synchronizing long data sets with minimal impact while the initial value method with time independent coupling tends to be substantially faster more flexible and easier to use we also describe a method of coupling which is useful for sparse experimental data sets our use of the colpitts oscillator allows us to explore in detail the case of a system with one positive lyapunov exponent the methods we explored are easily extended to driven systems such as neurons with time dependent injected current they are expected to be of value in nonchaotic systems as well software is available on request

a modified chua chaotic oscillator and its application to secure communications a new modification to the chua oscillator is proposed bifurcation diagrams poincare map and the lyapunov exponents are presented an application to secure communications is presented a synchronization scheme based on the modified oscillator is proposed system simulations are performed for analysis in this paper a new modified chua oscillator is introduced the original chua oscillator is well known for its simple implementation and mathematical modeling a modification of the oscillator is proposed in order to facilitate the synchronization and the encryption and decryption scheme the modification consists in changing the nonlinear term of the original oscillator to a smooth and bounded nonlinear function a bifurcation diagram a poincare map and the lyapunov exponents are presented as proofs of chaoticity of the newly modified oscillator an application to secure communications is proposed in which two channels are used numerical simulations are performed in order to analyze the communication system

parameter estimation in spatially extended systems the karhunen loeve and galerkin multiple shooting approach parameter estimation for spatiotemporal dynamics for coupled map lattices and continuous time domain systems is shown using a combination of multiple shooting karhunen loeve decomposition and galerkin s projection methodologies the resulting advantages in estimating parameters have been studied and discussed for chaotic and turbulent dynamics using small amounts of data from subsystems availability of only scalar and noisy time series data effects of space time parameter variations and in the presence of multiple time scales

adaptive feedback control algorithm this paper is motivated by giving the detailed proofs and some interesting remarks on the results the author obtained in a series of papers phys rev lett 93 214101 2004 phys rev e 71 037203 2005 69 067201 2004 where an adaptive feedback algorithm was proposed to effectively stabilize and synchronize chaotic systems this note proves in detail the strictness of this algorithm from the viewpoint of mathematics and gives some interesting remarks for its potential applications to chaos control a synchronization in addition a significant comment on synchronization based parameter estimation is given which shows some techniques proposed in literature less strict and ineffective in some cases

using waveform information in nonlinear data assimilation information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables after this learning period is complete one may predict the model response to new forces and when successful these predictions will match additional observations this adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient we discuss the use of information in the waveform of the data realized through a time delayed collection of measurements to provide additional stability and accuracy to this search procedure several examples are explored including a few familiar nonlinear dynamical systems and small networks of colpitts oscillators

chaos synchronization of double duffing systems with parameters excited by a chaotic signal chaos synchronization by driving parameter for two uncoupled identical chaotic double duffing systems is presented replacing two corresponding parameters of the identical systems by the same function of chaotic state variables of a third chaotic system the synchronization or anti synchronization of two uncoupled systems can be obtained numerical simulations are illustrated for either synchronization or anti synchronization of which the occurrence depends significantly on initial conditions and on driving strength alternative complete synchronization and anti synchronization is also discovered

synchronization based approach for parameters identification in delayed chaotic neural networks abstract in this paper an adaptive procedure to the problem of synchronization and parameters identification for chaotic neural networks with time varying delay is introduced by combining the adaptive control and linear feedback with appropriate update law based on the invariance principle of functional differential equations all the connection weight matrices can be efficiently estimated according to a simple rigorous and systematic technique this approach is also able to track the changes in the operating parameters of the experimental neural networks rapidly the speed of synchronization and parameters estimation can be adjusted under the adaptive gain properly chosen in addition the method is simple to implement in practice and it is quite robust against the effect of slight noise in the given time series and the estimated value of a parameter fluctuates around the correct value