direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

adaptive coupling and enhanced synchronization in coupled phase oscillators we study the dynamics of an adaptive coupled array of phase oscillators the adaptive law is designed in such a way that the coupling grows stronger for the pairs which have larger phase incoherence the proposed scheme enhances the synchronization and achieves a more reasonable coupling dynamics for the network of oscillators with different intrinsic frequencies the synchronization speed and the steady state phase difference can be adjusted by the parameters of the adaptive law besides global coupling nearest neighbor ring coupling is also considered to demonstrate the generality of the method

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

adaptive control and synchronization of identical new chaotic flows with unknown parameters via single input the single input linear feedback control for synchronizing two identical new 3d chaotic flows reported by li et al x f li k e chlouverakis d l xu nonlinear dynamics and circuit realization of a new chaotic flow a variant of lorenz chen and lu nonlinear analysis rwa 10 4 2009 2357 2368 is proposed in this paper sufficient conditions of synchronization are obtained for both linear feedback and adaptive control approaches the problem of adaptive synchronization between two nearly identical chaotic systems with unknown parameters is also studied based on the lyapunov stability theory two kinds of single input adaptive synchronization controllers are designed and the adaptive parameter update laws are developed

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

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

comment on adaptive feedback control algorithm we point out a problem in the parametric estimation method based on the adaptive feedback algorithm proposed by d huang phys rev e 73 066204 2006 both illustratively and analytically furthermore under some hypotheses we prove that it is not the so called chaotic dynamical characteristic but the linear independence between the right hand functions and the estimated parameters of the intrinsic system in its attractor that counts in the availability of this algorithm in estimating the unknown parameters

adaptive synchronization between two different hyperchaotic systems abstract this work presents chaos synchronization between two different hyperchaotic systems using adaptive control the sufficient conditions for achieving synchronization of two high dimensional chaotic systems are derived based on lyapunov stability theory and an adaptive control law and a parameter update rule for unknown parameters are given such that generalized henon heiles system is controlled to be hyperchaotic chen system theoretical analysis and numerical simulations are shown to verify the results

synchronization of spatiotemporal chaos with positive conditional lyapunov exponents computer simulations show that following the scalar driving approach synchronization of spatiotemporal chaos can also be achieved in driven subsystem with positive conditional lyapunov exponents this is a result of the so called extreme trap in the neighborhood of the maximum value the higher order term of difference causes a first order dissipative effect which is not reflected by the conditional lyapunov exponents hence the actual average divergence rate is smaller than the maximum conditional lyapunov number and thus causes the driven system to synchronize even when the conditional lyapunov exponents are positive

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 of a chaotic finance system synchronization strategies of a three dimensional chaotic finance system are investigated in this paper based on lyapunov stability theory and routh hurwitz criteria some effective controllers are designed for the global asymptotic synchronization on different conditions when the system parameters are known the hybrid feedback control and a method based on special matrix structure are adopted respectively to realize the synchronization of the chaotic finance system when the parameters are unknown the active control is extended and introduced to realize the synchronization numerical simulations show the validity and feasibility of the synchronization schemes

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

adaptive synchronization of cohen grossberg neural network with mixed time varying delays and stochastic perturbation in this paper based on the lasalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback technique several sufficient conditions ensuring the adaptive synchronization of cohen grossberg neural network with mixed time varying delays and stochastic perturbation are derived in particular the synchronization criterion considered globally is the almost surely asymptotic stability of the error dynamical system our synchronization criterion is easily verified and does not solve any linear matrix inequality these results generalized a few previous known results at last a numerical example and its simulations are provided to demonstrate the effectiveness and advantage of the theoretical results

a simple adaptive feedback scheme for identical synchronizing chaotic systems with uncertain parameters an adaptive feedback control scheme for identical synchronizing two linearly coupled chaotic systems and identifying uncertain parameters is proposed in comparison with the previous methods it inherited the present scheme is more flexible and accessible this is because that the prerequisites on the given chaotic systems are much looser and the adaptive feedback controllers involved are relatively independent moreover the present scheme is a thoroughly amendatory one by which the uncertain parameters can be identified three concrete chaotic systems are employed to show the effectiveness of the presented scheme in addition how the coefficient in the adaptive law affects the convergence rate and the final strength is studied numerically

chaos synchronization and parameter estimation of single degree of freedom oscillators via adaptive control this paper addresses the problem of synchronizing a class of single degree of freedom oscillators with uncertain parameters a modified adaptive control scheme is proposed to achieve globally asymptotic stable synchronization between the master and slave oscillators with arbitrary different initial conditions based on the barbalat s lemma one of the advantages of the method is that it requires only a scalar driving signal which may be easily designed in practical applications on the other hand the method can ensure that the unknown parameters in the slave oscillator would be completely estimated with an adaptive updating law numerical simulations are performed on two examples to verify the analytical results

adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters in this paper the problems of control and synchronization of a novel hyperchaotic system with uncertain parameters are studied based on the lyapunov stability theory and the adaptive control theory this uncertain hyperchaotic system is suppressed to its unstable equilibrium furthermore synchronization between two identical uncertain hyperchaotic systems is achieved by proposing an adaptive control law and a parameter estimation update law numerical simulations are presented to demonstrate the analytical results

nonlinear analytic semiflows in this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems x t f x t and quasilinear initial value problems x t a x t x t f x t this theory extends the theory of daprato and grisvard of 1979 and shows how various properties like analyticity of solutions can be derived as a direct corollary of the existence theorem

adaptive modified function projective synchronization of unknown chaotic systems with different order abstract this paper investigates the modified function projective synchronization mfps between two different dimensional chaotic systems with fully unknown or partially unknown parameters via increased order based on the lyapunov stability theorem and adaptive control method a unified adaptive controller and parameters update law can be designed for achieving the mfps of the two different chaotic systems with different orders numerical simulations are presented to show the effectiveness of the proposed synchronization scheme

parameter estimation through ignorance dynamical modeling lies at the heart of our understanding of physical systems its role in science is deeper than mere operational forecasting in that it allows us to evaluate the adequacy of the mathematical structure of our models despite the importance of model parameters there is no general method of parameter estimation outside linear systems a relatively simple method of parameter estimation for nonlinear systems is introduced based on variations in the accuracy of probability forecasts it is illustrated on the logistic map the henon map and the 12 dimensional lorenz96 flow and its ability to outperform linear least squares in these systems is explored at various noise levels and sampling rates as expected it is more effective when the forecast error distributions are non gaussian the method selects parameter values by minimizing a proper local skill score for continuous probability forecasts as a function of the parameter values this approach is easier to implement in practice than alternative nonlinear methods based on the geometry of attractors or the ability of the model to shadow the observations direct measures of inadequacy in the model the implied ignorance and the information deficit are introduced

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

parameter estimation of dynamical systems via a chaotic ant swarm through the construction of suitable objective function the parameter estimation of the dynamical system could be converted to the problem of parameter optimization based on the chaotic ant swarm optimization approach we investigate the problem of parameter optimization for the dynamical systems in the presence of noise we systematically analyze the basic relationships among the complexity of objective function the length of time series and the performance of the searching algorithm furthermore we consider the effect of measurable additive noise on the objective function numerical simulations are also provided to show the effectiveness and feasibility of the proposed methods

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

synchronizing the noise perturbed unified chaotic system by sliding mode control abstract in this paper synchronization between unidirectionally coupled unified chaotic systems with noise perturbation is investigated sufficient conditions of synchronization between these noise perturbed systems are established by means of the so called sliding mode control method some numerical simulations are also included to visualize the effectiveness and the feasibility of the developed approach

recovering unknown model parameters contained in a class of time variant chaotic dynamical systems abstract this work deals mainly with the problem of recovering all unknown parameters for a class of time variant chaotic dynamical systems from given time sequence based on synchronization between a chaotic sender system and an additional receiver system a procedure which combines a linear feedback technique with updated feedback gain and an adapted control strategy associated with the law of estimated parameters is developed to dynamically determine the values of unknown parameters contained in the sender system to promote widespread applications the structure of the receiver system can be independent of that of the sender system the effectiveness of this procedure is guaranteed by the periodic version of the classical lasalle invariance principle of differential equations illustrations are presented for a harmonically excited duffing oscillator and a four dimensional chaotic oscillator the numerical results reveal the present procedure not only can precisely recover unknown model parameters but also can rapidly response to sudden changes in unknown parameters in addition it has great robustness against the disturbance of noise

elementary backlund transformations nonlinear superposition formulae and algebraic construction of solutions for the nonlinear evolution equations solvable by the zakharov shabat spectral transform abstract novel nonlinear superposition formulae are given for solutions of the class of nonlinear evolution equations solvable via the spectral transform associated with the zakharov shabat spectral problem and an algebraic procedure is provided to construct solutions of these equations

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

backlund transformations for the schrodinger equation with a spectral dependence in the potential the schrodinger equation on the line with a potential depending linearly on the spectral parameter is considered it is shown that this spectral problem admits one parameter called elementary backlund transformations and two parameter called full backlund transformations the transformations of the spectral data under all these backlund transformations bts are explicitly computed different nonlinear superposition formulae for the different bts considered are given and used to obtain soliton solutions of the evolution equations associated with the spectral problem

chaos synchronization between two novel different hyperchaotic systems with unknown parameters this work is devoted to investigating the synchronization between two novel different hyperchaotic systems with fully unknown parameters i e an uncertain hyperchaotic lorenz system and an uncertain hyperchaotic lu system based on the lyapunov stability theory a new adaptive controller with parameter update law is designed to synchronize these two hyperchaotic systems asymptotically and globally numerical simulations are presented to verify the effectiveness of the synchronization scheme

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

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

synchronization with positive conditional lyapunov exponents synchronization of chaotic systems may occur only when the largest conditional lyapunov exponent of the driven system is negative the synchronization with positive conditional lyapunov exponents reported in a recent paper phys rev e 56 2272 1997 is a combined result of the contracting region of the system and the finite precision in computer simulations

structure identification of uncertain general complex dynamical networks with time delay it is well known that many real world complex networks have various uncertain information such as unknown or uncertain topological structure and node dynamics the structure identification problem has theoretical and practical importance for uncertain complex dynamical networks at the same time time delay often appears in the state variables or coupling coefficients of various practical complex networks this paper initiates a novel approach for simultaneously identifying the topological structure and unknown parameters of uncertain general complex networks with time delay in particular this method is also effective for uncertain delayed complex dynamical networks with different node dynamics moreover the proposed method can be easily extended to monitor the on line evolution of network topological structure finally three representative examples are then given to verify the effectiveness of the proposed approach

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 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

identifying the topology of networks with discrete time dynamics we suggest a method for identifying the topology of networks with discrete time dynamics based on the dynamical evolution supported by the networks the frobenius matrix norm and lasalle s invariance principle are used in this work the network concerned can be directed or undirected weighted or unweighted and the local dynamics of each node can be nonidentical the connections among the nodes can be all unknown or partially known finally several examples are illustrated to verify the theoretical results

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

evaluation of dynamical models dissipative synchronization and other techniques some recent developments for the validation of nonlinear models built from data are reviewed besides giving an overall view of the field a procedure is proposed and investigated based on the concept of dissipative synchronization between the data and the model which is very useful in validating models that should reproduce dominant dynamical features like bifurcations of the original system in order to assess the discriminating power of the procedure four well known benchmarks have been used namely duffing ueda duffingholmes and van der pol oscillators plus the henon map the procedure developed for discrete time systems is focused on the dynamical properties of the model rather than on statistical issues for all the systems investigated it is shown that the discriminating power of the procedure is similar to that of bifurcation diagrams which in turn is much greater than say that of correlation dimension but at a much lower computational cost

invariance principles allowing of non lyapunov functions for estimating attractor of discrete dynamical systems this technical note establishes several versions of invariance principles for describing the eventual dynamical behaviors of discrete dynamical systems instead of the requirement of the so called lyapunov functions in the classical lasalle invariance principle some more relaxed conditions are imported the established invariance principles thus can be applied to a more general class of discrete dynamical systems for classifying their orbits into two categories based on the eventual dynamical behaviors and the proposed classification scheme is suitable for theoretically and numerically estimating the local or global attractors produced by the discrete dynamical systems the practical usefulness of the analytical results is verified by systematically investigating several representative discrete systems

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

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

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

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

exponential h synchronization and state estimation for chaotic systems via a unified model in this paper h synchronization and state estimation problems are considered for different types of chaotic systems a unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems such as hopfield neural networks cellular neural networks chua s circuits unified chaotic systems qi systems chaotic recurrent multilayer perceptrons etc based on the h performance analysis of this unified model using the linear matrix inequality approach novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the state estimation problem is then studied for the same unified model where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level the parameters of these controllers and filters are obtained by solving the eigenvalue problem most chaotic systems can be transformed into this unified model and h synchronization controllers and state estimators for these systems are designed in a unified way three numerical examples are provided to show the usefulness of the proposed h synchronization and state estimation conditions

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

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

on hyperchaos synchronization of a hyperchaotic lu system abstract this work presents hyperchaos synchronization of two identical hyperchaotic lu systems in this study three methods are applied to achieve hyperchaos synchronization the sufficient conditions for achieving synchronization of two identical hyperchaotic lu systems are derived by using lyapunov stability theory numerical simulations are presented to demonstrate the effectiveness of the proposed hyperchaos synchronization schemes

optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems based on the lyapunov stability and adaptive synchronization theory optimization design of adaptive controllers and parameter observers with controllable gain coefficient are investigated in detail the linear errors of corresponding variables and parameters are used to construct different appropriate positive lyapunov functions v and the parameter observers and adaptive controllers are approached analytically by simplifying the differential inequality dv dt 0 particularly an optional gain coefficient is selected in the parameter observers and positive lyapunov function which decides the transient period to identify the unknown parameters and reach synchronization the scheme is used to study the synchronization of two non identical hyperchaotic rossler systems the theoretical and numerical results confirm that the four unknown parameters in the drive system are estimated exactly and the two hyperchaotic systems reach complete synchronization when the controllers and parameter observers work on the driven system to confirm the model independence of this scheme an alternative hyperchaotic system is investigated whereby the results confirm that the five unknown parameters are identified rapidly and exactly and that the two hyperchaotic systems reach complete synchronization as well

locating unstable periodic orbits when adaptation integrates into delayed feedback control finding unstable periodic orbits upos is always a challenging demand in biophysics and computational biology which needs efficient algorithms to meet this need an approach to locating unstable periodic orbits in chaotic dynamical system is presented the uniqueness of the approach lies in the introduction of adaptive rules for both feedback gain and time delay in the system without requiring any information of the targeted upo periods a priori this approach is theoretically validated under some mild conditions and successfully tested with some practical strategies in several typical chaotic systems with or without significant time delays

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

a new hyperchaotic system and its synchronization in this paper a four dimensional 4d continuous autonomous hyperchaotic system is introduced and analyzed this hyperchaotic system is constructed by adding a linear controller to the 3d autonomous chaotic system with a reverse butterfly shape attractor some of its basic dynamical properties such as lyapunov exponents poincare section bifurcation diagram and the periodic orbits evolving into chaotic hyperchaotic dynamical behavior by varying parameter d are studied furthermore the full state hybrid projective synchronization fshps of new hyperchaotic system with unknown parameters including the unknown coefficients of nonlinear terms is studied by using adaptive control numerical simulations are presented to show the effective of the proposed chaos synchronization scheme

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

adaptive control and synchronization of a modified chua s circuit system this study addresses the adaptive control and synchronization of the modified chua s circuit system with unknown system parameters adaptive control law is applied to suppress chaos to one of the three steady states adaptive control law is applied to achieve synchronization of two identical modified chua s circuit systems routh hurwitz criteria and lyapunov direct method are used to study the asymptotic stability of the steady states numerical simulations are included to show the effectiveness of the proposed control method

reconstruction of complex networks with delays and noise perturbation based on generalized outer synchronization this paper proposes an approach to identify the topological structure and unknown system parameters of a weighted complex dynamical network with delay and noise perturbation based on the barbalat type invariance principle for stochastic differential equations an effective adaptive feedback technique with an updated law is developed to realize generalized outer synchronization the unknown topological structure and parameters are identified simultaneously through the established technique the weight configuration matrix was found to be unnecessarily symmetric numerical examples are examined to illustrate the effectiveness of the analytical results

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

the hele shaw problem and area preserving curve shortening motions we prove existence locally in time of a solution of the following hele shaw problem given a simply connected curve contained in a smooth bounded domain find the motion of the curve such that its normal velocity equals the jump of the normal derivatives of a function which is harmonic in the complement of the curve in and whose boundary value on the curve equals its curvature we show that this motion is a curve shortening motion which does not change the area of the region enclosed by the curve in case is the whole plane 2 we also show that if the initial curve is close to an equilibrium curve i e to a circle then there exists a global solution and the global solution tends to some circle exponentially fast as time tends to infinity

soliton solutions for two nonlinear partial differential equations using a darboux transformation of the lax pairs two darboux transformations of the 1 1 dimensional wu zhang wz equation and the two component camassa holm 2ch system with the reciprocal transformation are obtained one loop and two loop soliton solutions and multisoliton like solutions of the 2ch system are obtained by using the darboux transformations and selecting different seed solutions of the corresponding equations the bidirectional soliton solutions of the 1 1 dimensional wz equation are also obtained the interactions of two soliton head on and overtaking collisions for the wz equation and the evolution of the two soliton like solutions for the 2ch system are studied

theoretical and experimental time series analysis of an inductorless chua s circuit abstract in this paper we have analyzed the time series obtained from an experimental realization of an inductorless version of chua s circuit we have also compared the experimental results with the results emerging by analysis of the time series obtained by numerical simulations of the respective model equations lyapunov exponent spectra the kaplan yorke dimension and phase space diagrams were used to show the similarities between theoretical and experimental results we were able to identify the effects of the operational amplifier simulated inductor internal resistance on the chua s circuit dynamics decreasing internal resistance for decreasing current through the circuit was responsible for the observed bifurcation route

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

a simple universal adaptive feedback controller for chaos and hyperchaos control a simple universal adaptive feedback controller is proposed for chaos control in comparison with previous methods the proposed scheme which uses a single feedback gain and converges very fast is suitable for application to a larger class of chaotic hyperchaotic and nonhyperbolic chaotic systems a sufficient condition for selecting the least feedback terms is given and a numerical example using the lorenz system verifies the correctness and effectiveness of the proposed approach

analysis of spurious synchronization with positive conditional lyapunov exponents in computer simulations abstract synchronization of chaotic systems has been a field of great interest and potential applications the necessary condition for synchronization is the negativity of the largest conditional lyapunov exponent some researches have shown that negativity of the largest conditional lyapunov exponent is not a sufficient condition for high quality synchronization in the presence of small perturbations however it was reported that synchronization can be achieved with positive conditional lyapunov exponents based on numerical simulations in this paper we first analyze the behavior of synchronization with positive conditional lyapunov exponents in computer simulations of the synchronization of chaotic systems with various couplings and demonstrate that synchronization is an outcome of finite precision in numerical simulations it is shown that such a numerical artifact is quite common and easily occurs in numerical simulations thus can be confusing and misleading some behavior and properties of the synchronized system with slightly positive conditional lyapunov exponents can be understood based on the theory of on off intermittency we also study the effects of finite precision on numerical simulation of on off intermittency special care should be taken in numerical simulations of chaotic systems in order not to mistake numerical artifacts as physical phenomena

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

stochastic adaptive synchronization for time varying complex delayed dynamical networks with heterogeneous nodes stochastic synchronization for a time varying complex delayed dynamical networks with heterogeneous nodes is studied in this paper using adaptive synchronization scheme for detailed analysis and discussion based on lyapunov stability theory the properties of weiner process brownian motions some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of the complex delayed dynamical networks model a sufficient condition is given to ensure that the proposed controlled networks model is globally asymptotically synchronized in mean square sense a simulation example is presented to show the effectiveness and applicability of the proposed results

adaptive complete synchronization of the noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch in this paper we design an adaptive feedback controller to synchronize a class of noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch based on invariance principle of stochastic time delay differential equations some sufficient conditions of adaptive complete synchronization are given comparing with other papers here we consider the effect of internal noise time delay and parametric mismatch in the synchronized process as the illustrative examples the famous lorenz system and rossler system are considered here in order to validate the proposed scheme numerical simulations are performed and the numerical results show that our scheme is very effective

backlund transformations related to the kaup newell spectral problem abstract a hierarchy of isospectral deformation equations related to the kaup newell spectral problem is obtained the generalized gauge transformations of the eigenmatrix of the spectral problem are used to generate backlund and self backlund transformations in a special case the backlund transformation of the null solution for all the equations in the hierarchy has been explicitly solved

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

impulsive synchronization of reaction diffusion neural networks with mixed delays and its application to image encryption this paper presents a new impulsive synchronization criterion of two identical reaction diffusion neural networks with discrete and unbounded distributed delays the new criterion is established by applying an impulse time dependent lyapunov functional combined with the use of a new type of integral inequality for treating the reaction diffusion terms the impulse time dependent feature of the proposed lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction diffusion neural networks than the conventional impulse time independent lyapunov functions functionals while the new integral inequality which is derived from wirtinger s inequality overcomes the conservatism introduced by the integral inequality used in the previous results numerical examples demonstrate the effectiveness of the proposed method later the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image the experimental results verify that the proposed image encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks

synchronization between adaptively coupled systems with discrete and distributed time delays this paper investigates complete synchronization of unidirectionally and adaptively coupled systems with discrete and distributed time delays instead of the conventional hypothesis of a uniform lipschitz condition on the system s vector fields only a local lipschitz condition is adopted it is proved that the local complete synchronization can be achieved through a unidirectional and adaptive coupling and that the global complete synchronization can be realized when the nonlinear degree of the vector fields is smaller than some derived critical value the results are illustrated in some representative models with time delays also considered is complete synchronization with an exponential convergence rate on the adaptively coupled time delayed systems with vector fields that are one sided uniformly lipschitz systems of this type can admit time varying discrete and distributed delays all the results can be further generalized to various types of synchronization between bidirectionally coupled time delayed systems or among delayed kinetic systems of a complex network