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

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

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

fast algorithms for close to toeplitz plus hankel systems and two sided linear prediction the low displacement rank definition of close to toeplitz ct matrices is extended to close to toeplitz plus hankel ctph matrices fast algorithms for solving ctph systems of equations are presented a matrix is defined as ctph if the sum of a ct matrix and a second ct matrix postmultiplied by an exchange matrix an equivalent definition in terms of uv rank is also given this definition is motivated by the application of the algorithms to two sided linear prediction tsp autocorrelation and covariance forms of tsp analogous to those for one sided linear prediction osp are defined the covariance form of tsp is solved using the ctph fast algorithms just as the covariance form of osp is solved using ct fast algorithms numerical examples show that tsp produces smaller residuals than osp and resolves sharp spectral peaks better than osp and that covariance tsp produces smaller residuals than autocorrelation tsp

eigenvalue problems for nonlinear differential equations on a measure chain abstract values of are determined for which there exist positive solutions of the second order differential equation on a measure chain u t a t f u t 0 t 0 1 satisfying either the conjugate boundary conditions u 0 u 1 0 or the right focal boundary conditions u 0 u 1 0 where a and f are positive valued and both lim x 0 f x x and lim x f x x exist

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

on boundary value problems of second order perturbed dynamic inclusions on time scales abstract in this paper an existence criterion is established for a class of second order perturbed dynamic inclusions on time scales with boundary conditions the main approach is a fixed point theorem for multi valued maps due to dhage

multiple positive solutions for p laplacian m point boundary value problems on time scales let t be a time scale such that 0 email protected t a i 0 for i 1 m 2 let x i satisfy 0 x 1 x 2 x m 2 r t and i 1 m 2a i 1 we consider the following p laplacian m point boundary value problem on time scales f p u d t a t f t u t 0 email protected 0 t u 0 0 f p u d t email protected i 1m 2a email protected p u d x i where email protected c l d 0 t 0 and email protected c l d 0 t x 0 0 some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying avery henderson and leggett williams fixed point theorems respectively in particular our criteria extend and improve some known results

lmi optimization approach to stabilization of genesio tesi chaotic system via dynamic controller abstract in this paper a design method for a new controller to control the genesio tesi chaotic systems is proposed in this work a dynamic outputs feedback controller for the system is developed for the first time for stability analysis a well known lyapunov stability theorem combining with lmi linear matrix inequality optimization approach is utilized a numerical simulation is presented to show the usefulness of the proposed control scheme

numerical continuation of bifurcations of limit cycles in matlab rm cl matcont and matcont are matlab continuation packages for the interactive numerical study of a range of parameterized nonlinear dynamical systems in particular odes matcont is an interactive graphical package and rm cl matcont is a commandline version both packages allow us to compute curves of equilibria limit points hopf points limit cycles flip fold and torus bifurcation points of limit cycles we discuss computational details of the continuation of limit cycles and flip fold and torus bifurcations of limit cycles in matcont and rm cl matcont using orthogonal collocation instead of the more commonly used fully extended systems we use minimally extended systems we further describe the use of the matlab sparse matrix routines and the initialization and adaptation of the bordering vectors that are essential in minimally extended systems finally we compare the use of the minimally and the fully extended systems in the matlab environment

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

existence of triple positive solutions to a class of p laplacian boundary value problems abstract by using leggett williams fixed point theorem a class of p laplacian boundary value problem is studied sufficient conditions for the existence of triple positive solutions are established

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

simple feedback systems with chaotic behaviour abstract an example is given of a second order dynamical system containing a relay with hysteresis which can display chaotic motion it is shown that this system can be approximated by a third order model with a continuous non linearity which appears to behave in a similar manner

multiband least squares fir filter design this paper gives two methods for the least squares approximation design of fir digital filters they both allow multiple pass and stop bands and arbitrary transition bands all with explicit control of band edges the first method is as simple to use as a window method this design method builds up an optimal multiband frequency response by sequentially adding and subtracting optimal lowpass filters with transition bands however it assumes the ideal response has spline transition functions and does not allow error weighting the second method allows different weights in the multiple passbands stopbands and transition bands but it requires numerical solution of simultaneous equations which may be ill conditioned these methods compliment the parks mcclellan algorithm which minimizes the chebyshev error

linear interpolation lattice for nonstationary signals a ladder algorithm for linear interpolation of nonstationary signals is developed the algorithm is based on the sliding window least squares method and can be implemented using a lattice structure furthermore by assuming that the input signal is stationary the number of parameters required to be calculated is reduced the lattice structure in the case of stationary input is also presented

positive solutions for a nonlinear functional dynamic equation on a time scale abstract in this paper we obtain sufficient conditions for the existence of positive solutions to a nonlocal eigenvalue problem for a class of nonlinear functional dynamic equations on a time scale we employ a cone theoretic fixed point theorem to establish our results

numerical periodic normalization for codim 1 bifurcations of limit cycles explicit computational formulas for the coefficients of the periodic normal forms for all codim 1 bifurcations of limit cycles in generic autonomous odes are derived they include second order coefficients for the fold limit point bifurcation as well as third order coefficients for the flip period doubling and neimark sacker torus bifurcations the formulas are independent of the dimension of the phase space and involve solutions of certain boundary value problems on the interval 0 t where t is the period of the critical cycle as well as multilinear functions from the taylor expansion of the right hand sides near the cycle the formulas allow us to distinguish between sub and supercritical bifurcations in agreement with earlier asymptotic expansions of the bifurcating solutions our formulation makes it possible to use robust numerical boundary value algorithms based on orthogonal collocation rather than shooting techniques which greatly expands its applicability the actual implementation is described in detail we include three numerical examples in which codim 2 singularities are detected along branches of codim 1 bifurcations of limit cycles as zeros of the periodic normal form coefficients

computing theoretical autocovariances of multivariate autoregressive moving average models by using a block levinson method a closed form expression relating the theoretical autocovariances of a multivariate autoregressive moving average arma model to the arma parameters in terms of a system of linear equations has been presented recently using this result and the special hankel plus toeplitz structure of the coefficient matrix obtained after suitable partitioning this paper presents a method for computing multivariate autocovariance functions that is based on a block levinson procedure the method is particularly advantageous for models with high order autoregressive components and or a large number of variables

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on time scales in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value pr

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

a simple adaptive feedback control method for chaos and hyper chaos control abstract this paper investigates the problem of chaos and hyper chaos control and proposes a simple adaptive feedback control method for chaos control under a reasonable assumption in comparison with previous methods the present control technique is simple both in the form of the controller and its application several illustrative examples with numerical simulations are studied by using the results obtained in this paper study of examples shows that our control method works very well in chaos control

inversion of certain extensions of toeplitz matrices it is shown how an algorithm for inverting toeplitz matrices using o n2 operations can be modified to deal with a certain type of extension named conjugate toeplitz matrices the block partitioned case is also included

positive solutions for p laplacian functional dynamic equations on time scales abstract in this paper the authors study the boundary value problems for a p laplacian functional dynamic equation on a time scale p x t a t f x t x t 0 t 0 t x 0 t t t r 0 x 0 b 0 x 0 x t 0 by using the twin fixed point theorem sufficient conditions are established for the existence of twin positive solutions

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

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

triple positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales in this paper we present sufficient conditions for the existence of at least three positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale to show our main results we apply a new fixed point theorem due to avery and peterson three positive fixed points of nonlinear operators on ordered banach spaces comput math appl 42 2001 313 322

a weighted least squares algorithm for quasi equiripple fir and iir digital filter design it has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of a finite impulse response fir filter the weighted least squares solution is equiripple the crux of the problem lies in the determination of the necessary least squares frequency response weighting function a novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi equiripple design is presented the algorithm converges very rapidly it typically produces a design which is only about 1 db away from the minimax optimum solution in two iterations and converges to within 0 1 db in six iterations convergence speed is independent of the order of the filter it can be used to design filters with arbitrarily prescribed phase and amplitude response

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on the half line in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value problems on the half line f u a t f u t 0 0r is the increasing homeomorphism and positive homomorphism and f 0 0 we show the sufficient conditions for the existence of countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

three positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales abstract in this paper existence criteria of three positive solutions to the following boundary value problems for p laplacian dynamic equations on time scales p u t a t f u t 0 t 0 t t u 0 0 u t b 1 u 0 or u 0 b 0 u 0 u t 0 are established by using the well known leggett williams fixed point theorem an example is also given to illustrate the main results

models of complex dynamics in nonlinear systems abstract a study of complex dynamics in a simple important class of nonlinear systems has been developed the well known phenomena of period doubling and homoclinic orbit have been analysed and simple conditions approximate in nature for their occurrence are derived they allow one to establish some connections of such complex behaviours with structural characteristics of the considered systems as shown by two detailed application examples

efficient solution of a toeplitz plus hankel coefficient matrix system of equations there are well known fast algorithms such as the levinson recursion for solving linear equations with a toeplitz or hankel coefficient matrix this paper extends the saving obtained by the levinson recursion for inversion of a toeplitz matrix to problems involving the inversion of matrices which are the sum of toeplitz and hankel matrices

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

the harmonic balance method for bifurcation analysis of large scale nonlinear mechanical systems abstract the harmonic balance hb method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems the objective of this paper is to exploit the method for bifurcation analysis i e for the detection and tracking of bifurcations of nonlinear systems to this end an algorithm that combines the computation of the floquet exponents with bordering techniques is developed a new procedure for the tracking of neimark sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed the hb method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device

bifurcation analysis via harmonic balance in periodic systems with feedback structure the harmonic balance approach is applied to a class of periodic dynamical systems with a specific but quite general feedback structure in order to analyse approximately tangent saddle node and flip period doubling bifurcations of periodic solutions by exploiting the system structure an algebraic system of equations whose unknowns are the coefficients of a truncated fourier series is defined and the relationship between the bifurcations of the roots of this algebraic system and the tangent and flip bifurcations of the periodic solutions is pointed out an example concerning an adaptive control system illustrates the proposed methodology

kernel structure of toeplitz plus hankel matrices abstract the structure of the kernel of block toeplitz plus hankel matrices r aj k bj k where aj and bj are the given p q blocks with entries from a given field is investigated it is shown that r corresponds to two systems of at most p q vector polynomials from which a basis of the kernel of r and all other toeplitz plus hankel matrices with the same parameters aj and bj can be built the main result is an analogue of a known kernel structure theorem for block toeplitz and block hankel matrices

harmonic balance analysis of period doubling bifurcations with implications for control of nonlinear dynamics the harmonic balance method is applied to the analysis of period doubling bifurcations in a general class of nonlinear feedback systems compact conditions for the prediction and stability analysis of period doubling bifurcations are obtained specializations of these conditions for systems in which the nonlinear subsystem is static are given the implications of the results to control design are illustrated through the development of a design procedure for solving a representative control problem the objectives of the control design can include delay of a given period doubling bifurcation as well as stability objectives the results are illustrated with a detailed example

existence of three positive solutions to a second order boundary value problem on a measure chain growth conditions are imposed on f such that the boundary value problem x t f x t t t1 t2 x t1 x t1 0 and x t2 x t2 0 where t1 t2 from a measure chain t has at least three positive solutions by way of the five functionals fixed point theorem

multiple positive solutions for p laplacian functional dynamic equations on time scales abstract the authors improve some well known fixed point theorems and study the boundary value problems for a p laplacian functional dynamic equation on a time scale p x t a t f x t x t 0 t 0 t x 0 t t t r 0 x 0 b 0 x 0 0 x t 0 by using the fixed point theorems sufficient conditions are established for the existence of multiple positive solutions

anti synchronization of two different chaotic systems abstract in this paper the anti synchronization of two different chaotic systems is investigated on the basis of a nonlinear control scheme and lyapunov theory sufficient conditions for the stability of the error dynamics are derived where the controllers are designed by using the sum of the relevant variables in chaotic systems numerical simulations are performed for the genesio rossler system to demonstrate the effectiveness of the proposed control strategy

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

an l_1 method for the design of linear phase fir digital filters this paper considers the design of linear phase finite impulse response digital filters using an l1 optimality criterion the motivation for using such filters as well as a mathematical framework for their design is introduced it is shown that l1 filters possess flat passbands and stopbands while keeping the transition band comparable to that of least squares filters the uniqueness of l1 based filters is explored and an alternation type theorem for the optimal frequency response is derived an efficient algorithm for calculating the optimal filter coefficients is proposed which may be viewed as the analogue of the celebrated remez exchange method a comparison with other design techniques is made demonstrating that the l1 approach may be a good alternative in several applications

existence of solutions for a first order p laplacian bvp on time scales we introduce a first order delta dynamic equation on time scales involving the one dimensional p laplacian and prove the existence of at least one positive solution an example applying our result is also given

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

fast algorithms for linear prediction and system identification filters with linear phase a general finite impulse response fir filter can be used as a linear prediction filter if given only an input sample sequence or as a system identification model if given the input and output sequences from an unknown system with known correlation the coefficients of the fir filter that minimize the mean square error in both applications are found by solution of a set of normal equations with toeplitz structure using only data samples the coefficients that yield the least squared error in both applications are found by solution of a set of normal equations with near to toeplitz structure computationally efficient fast algorithms have been published to solve for the coefficients from both types of normal equation structures if the fir filter is constrained to have a linear phase then the impulse response must be symmetric this then leads to normal equations with toeplitz plus hankel or near to toeplitz plus hankel structure fast algorithms for solving these normal equations for the filter coefficients are developed in this paper they have computational complexity proportional to m2and parameter storage proportional to m where m is the filter order an application of one of these algorithms for spectral estimation concludes the paper

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

triple positive pseudo symmetric solutions of three point bvps for p laplacian dynamic equations on time scales abstract let t be a time scale such that 0 t t we consider the three point boundary value problem for p laplacian dynamic equations on time scales t of the form p u t h t f t u t 0 for t 0 t t with boundary conditions u 0 0 u u t where t is symmetric in t t and p u u p 2 u with p 1 by using a pseudo symmetric technique and the five functionals fixed point theorem we prove that the boundary value problem has at least three positive pseudo symmetric solutions under some assumptions as an application an example is given to illustrate the result

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

adaptive backstepping synchronization between chaotic systems with unknown lipschitz constant abstract the error between two nonlinear terms is a key point of many synchronization problems however the lipschitz constant of the nonlinear term is not always easy to calculate for the stability analysis of the controlled error system thus the nonlinear systems with unknown parameters and unknown lipschitz constant is considered in this paper their scalar synchronous controller is proposed based on the thought of backstepping design without the need to evaluate the invariant set and calculate the lipschitz constant an assistant adaptive estimator is designed for the lipschitz constant what s more as a problem solving skill two different estimators are used on the same unknown parameter finally the synchronization control for both chaotic autonomous van der pol duffing advp systems and chaotic genesio systems with unknown parameters are given as examples to verify the control effect

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

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

displacement in the parameter space versus spurious solution of discretization with large time step in order to investigate a possible correspondence between differential and difference equations it is important to possess discretization of ordinary differential equations it is well known that when differential equations are discretized the solution thus obtained depends on the time step used in the majority of cases such a solution is considered spurious when it does not resemble the expected solution of the differential equation this often happens when the time step taken into consideration is too large in this work we show that even for quite large time steps some solutions which do not correspond to the expected ones are still topologically equivalent to solutions of the original continuous system if a displacement in the parameter space is considered to reduce such a displacement a judicious choice of the discretization scheme should be made to this end a recent discretization scheme based on the lie expansion of the original differential equations proposed by monaco and normand cyrot will be analysed such a scheme will be shown to be sufficient for providing an adequate discretization for quite large time steps compared to the pseudo period of the underlying dynamics

controlling chaotic and hyperchaotic systems via a simple adaptive feedback controller this paper investigates the problem of chaos control and proposes a simple adaptive feedback control method for it under a reasonable assumption in comparison with previous methods the present control technique is simple both in the form of the controller and in its application a numerical example using the genesio chaotic system verifies the effectiveness and correctness of the proposed approach

chaotification via system immersion by introducing a definition of partially chaotic for a kind of generalized chaotic system this paper discusses the chaotification problem with a new approach based on system immersion and manifold invariance the basic idea is to immerse the plant system into a reduced order chaotic system the proposed approach is also applied to chaotify systems with uncertain parameters illustrative examples with simulation results are presented to validate the proposed chaotification schemes

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

harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems abstract the paper considers the problem of determining the conditions under which a nonlinear dynamical system can give rise to a chaotic behaviour on the basis of the harmonic balance principle which is widely used in the frequency analysis of nonlinear control systems two practical methods are presented for predicting the existence and the location of chaotic motions this is formulated as a function of the system parameters when the system structure is fixed by rather general input output or state equation models several examples of application are presented to show the rather straightforward computations involved in the proposed methods the kind of results which can be obtained and due to the heuristic approach to the problem their corresponding approximation

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

existence theory for positive solutions to one dimensional p laplacian boundary value problems on time scales abstract in this paper we consider the one dimensional p laplacian boundary value problem on time scales p u t h t f u t 0 t a b u a b 0 u a 0 u b 0 where p u is p laplacian operator i e p u u p 2 u p 1 some new results are obtained for the existence of at least single twin or triple positive solutions of the above problem by using krasnosel skii s fixed point theorem new fixed point theorem due to avery and henderson and leggett williams fixed point theorem this is probably the first time the existence of positive solutions of one dimensional p laplacian boundary value problems on time scales has been studied

basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling abstract this article investigates both basic qualitative and basic quantitative properties of solutions to first and higher order dynamic equations on time scales and thus provides a foundation and framework for future advanced nonlinear studies in the field particular focus lies in the existence uniqueness dependency approximation and explicit representation of solutions to nonlinear initial value problems the main tools used are from modern areas of nonlinear analysis including the fixed point theorems of banach and schafer the method of successive approximations a novel definition of measuring distance in metric spaces and normed spaces and a separation of variables technique is introduced to the general time scale setting the new results compliment and extend those of stefan hilger s seminal paper of 1990 as an application of the new results we present and analyse a simple model from economics known as the keynesian cross model with lagged income in the general time scale environment ideas suggesting further applications and possible new directions for the novel results are also presented

fast singular value shrinkage with chebyshev polynomial approximation based on signal sparsity we propose an approximation method for thresholding of singular values using chebyshev polynomial approximation cpa many signal processing problems require iterative application of singular value decomposition svd for minimizing the rank of a given data matrix with other cost functions and or constraints which is called matrix rank minimization in matrix rank minimization singular values of a matrix are shrunk by hard thresholding soft thresholding or weighted soft thresholding however the computational cost of svd is generally too expensive to handle high dimensional signals such as images hence in this case matrix rank minimization requires enormous computation time in this paper we leverage cpa to approximately manipulate singular values without computing singular values and vectors the thresholding of singular values is expressed by a multiplication of certain matrices which is derived from a characteristic of cpa the multiplication is also efficiently computed using the sparsity of signals as a result the computational cost is significantly reduced experimental results suggest the effectiveness of our method through several image processing applications based on matrix rank minimization with nuclear norm relaxation in terms of computation time and approximation precision

fast and stable least squares approach for the design of linear phase fir filters we present a new numerical algorithm for solving the normal equations associated with the least squares design of linear phase fir filters the usual solution methods have a computational complexity of o n sup 3 moreover solving the normal equations with gaussian elimination commonly yields numerical errors especially when the filter is long here we convert a least squares method into the problem of constructing a system of orthonormal functions the proposed design algorithm needs only o n sup 2 computations and numerical errors can be reduced some examples are given to show the performance of the algorithm

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

fast triangular factorization of the sum of quasi toeplitz and quasi hankel matrices abstract the literature contains several recent fast algorithms for the triangular factorization of strongly regular toeplitz plus hankel matrices in this paper we study the rather more general sum of quasi toeplitz and quasi hankel matrices both hermitian and non hermitian quasi toeplitz and quasi hankel matrices are those that are congruent to toeplitz and hankel matrices in a special sense the derivation is based on the concept of displacement structure and its intimate relation to the schur reduction procedure for triangular factorization various special cases covering displacement ranks from two to eight are considered several other problems e g factorization of the inverse matrix solution of exact or overdetermined linear systems can be reduced to the direct factorization problem

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

least squared error fir filter design with transition bands the authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least squared error fir digital filters with an explicit control of the transition band edges design formulas are derived for approximations to ideal frequency responses which use pth order spline transition functions a mixed analytical and numerical method for zero error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived a variable order spline transition function is developed and a method for choosing the optimal order to minimize the integral squared approximation error is given

multiple positive solutions for functional dynamic equations on time scales in this paper we study the following functional dynamic equation on time scales f u d t a t f u t u m t 0 email protected 0 t t u t email protected t email protected r 0 t u 0 b 0 u d 0 0 u d t 0 where f r r is an increasing homeomorphism and a positive homomorphism and f 0 0 by using the well known leggett williams fixed point theorem existence criteria for multiple positive solutions are established an example is also given to illustrate the main results

triple positive solutions of m point bvps for p laplacian dynamic equations on time scales abstract this paper is concerned with the existence of positive solutions of p laplacian dynamic equation p u t a 1 t f u t 0 subject to boundary conditions u 0 b 0 i 1 m 2 a i u i 0 u t 0 or u 0 0 u t b 1 i 1 m 2 b i u i 0 where p v v p 2 v with p 1 by using the five functionals fixed point theorem we prove that the boundary value problem has at least three positive solutions as an application an example is given to illustrate the result

a hermitian toeplitz matrix is unitarily similar to a real toeplitz plus hankel matrix two unitary matrices are presented that transform a hermitian toeplitz matrix into a real toeplitz plus hankel matrix and vice versa additional properties and consequences of these unitary transformations are also presented for a certain class of n dimensional toeplitz plus hankel systems of equations an efficient method of solution is presented an example is given to illustrate the similarity transforms toeplitz plus hankel systems arise in a wide variety of applications such as linear filtering theory discrete inverse scattering and discretization of certain integral equations arising in mathematical physics

sturm liouville eigenvalue problems on time scales for sturm liouville eigenvalue problems on time scales with separated boundary conditions we give an oscillation theorem and establish rayleigh s principle our results not only unifly the corresponding theories for differential and difference equations but are also new in the discrete case

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

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

double positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales a new double fixed point theorem is applied to investigate the existence of at least double positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale