Adaptive Projective Synchronization Research Articles

Adaptive finite-time projective synchronization of complex networks with nonidentical nodes and quantized time-varying delayed coupling

This paper investigates the asymptotic projective synchronization and finite-time projective synchronization (FPS) of complex networks (CNs) with nonidentical nodes and quantized time-varying delayed coupling. Adaptive control method and finite-time stability theory are employed to design a novel adaptive controller and its adaptive law. The effectiveness and stability of the proposed adaptive controller are demonstrated through rigorous derivations based on Lyapunov stability theory and non-smooth analysis. It is indispensable that through numerical simulation experiments and comparative analysis, we verify the validity of the theoretical results and show the proposed adaptive controller can realize the synchronization of CNs with different nodes. This study holds significant theoretical value and practical relevance for understanding and controlling CNs with quantized time-varying delayed coupling.

Exponential projective synchronization analysis for quaternion-valued memristor-based neural networks with time delays

<abstract><p>The issues of exponential projective synchronization and adaptive exponential projective synchronization are analyzed for quaternion-valued memristor-based neural networks (QVMNNs) with time delays. Different from the results of existing decomposition techniques, a direct analytical approach is used to discuss the projection synchronization problem. First, in the framework of measurable selection and differential inclusion, the QVMNNs is transformed into a system with parametric uncertainty. Next, the sign function related to quaternion is introduced. Different proper control schemes are designed and several criteria for ascertaining exponential projective synchronization and adaptive exponential projective synchronization are derived based on Lyapunov theory and the properties of sign function. Furthermore, several corollaries about global projective synchronization are proposed. Finally, the reliability and validity of our results are substantiated by two numerical examples and its corresponding simulation.</p></abstract>

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization (ATVMPS) of different dimensional chaotic systems (DDCSs) with time delays and unknown parameters. Firstly, to estimate the unknown parameters, adaptive parameter updated laws are designed. Secondly, to realize the fixed-time ATVMPS of the time-delayed DDCSs, an adaptive delay-unrelated controller is designed, where time delays of chaotic systems are known or unknown. Thirdly, some simple fixed-time ATVMPS criteria are deduced, and the rigorous proof is provided by employing the inequality technique and Lyapunov theory. Furthermore, the settling time of fixed-time synchronization (Fix-TS) is obtained, which depends only on controller parameters and system parameters and is independent of the system’s initial states. Finally, simulation examples are presented to validate the theoretical analysis.

An investigation on microscopic chaos controlling of identical chemical reactor system via adaptive controlled hybrid projective synchronization

An investigation on microscopic chaos controlling of identical chemical reactor system via adaptive controlled hybrid projective synchronization

Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field

This paper focuses on investigating quaternion projective synchronization of the fractional order delayed quaternion valued neural networks(FODQVNN). By applying Lyapunov direct method rather than decomposition method, quaternion projective synchronization of FODQVNN is discussed, in which the projective coefficient is set to quaternion number. Through designing appropriate adaptive controllers, some succinct criteria ascertaining the quaternion projective synchronization issues for considering systems are obtained. Finally, an example is presented to test the effectiveness of the theoretical scheme.

Adaptive projective synchronization for a class of switched chaotic systems

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.

A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems

This paper investigates adaptive active control projective synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system for the identical structural chaotic systems. It is the first time that the active synchronization, the projective synchronization, and the adaptive synchronization are combined to achieve the synchronization of chaotic systems, which extend the control capability of achieving chaotic synchronization. By using a constant diagonal matrix, the active control is developed. Especially, when designing the controller, we just need to ensure that the diagonal elements of the diagonal matrix are less than or equal 0. So, the synchronization of chaotic systems can be realized more easily. Furthermore, by proposing an active controller, in combination with several different control schemes, we lower the complexity of the design process of the controller. More importantly, the larger the absolute value of product of the diagonal elements of diagonal matrix is, the smoother the curve of chaotic synchronization is and the shorter the time of chaotic synchronization is. In our paper, we take Lorenz system as an example to verify the effectiveness of the proposed synchronization scheme. Theoretical analysis and numerical simulations demonstrate the feasibility of this control method.

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems.

Hyperchaotic Analysis and Adaptive Projective Synchronization of Nonlinear Dynamical System

In this paper, a new nonlinear dynamical system has been studied which is obtained from the 3D chaotic system. The hyperchaotic analysis of the new system is checked in terms of dissipation, equilibrium points and their stability, Lyapunov exponent, time series, phase portraits, Poincare section and bifurcation diagram. Furthermore, the adaptive projective synchronization technique is used to synchronize the novel hyperchaotic system. A brief theoretical analysis and simulation results are presented to prove the behavior of the novel hyperchaotic system.

Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications

In this paper, the adaptive projective synchronization of time-delayed fractional-order neural networks is considered. Using the active control and adaptive control methods, efficient hybrid control strategies are designed for time-delayed fractional-order neural networks with uncertain parameters. Based on a new version of fractional-order Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities, which is easily checked and applied to practical systems. Finally, numerical simulations and application of the proposed methods to secure communications have been presented to validate the synchronization method.

Adaptive Functional Projective Lag Synchronization of Lorenz System

This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results. Keywords—Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method

Hidden attractors without equilibrium and adaptive reduced-order function projective synchronization from hyperchaotic Rikitake system

By introducing an additional state feedback into classic Rikitake system, a new hyperchaotic system without equilibrium is derived. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincare maps. Based on adaptive control and Lyapunov stability theory, we design a reduced-order projective synchronization scheme for synchronizing the hyperchaotic Rikitake system coexisting without equilibria and the original classic Rikitake system coexisting with two non-hyperbolic equilibria. Finally, numerical simulations are given to illustrate the effectiveness of the proposed synchronization scheme.

Hybrid adaptive function projective synchronization of a hyper Lüchaotic system

In this paper, a hybrid adaptive function projective synchronization of a hyper Lu chaotic system is investigated. Firstly, according to the Lyapunov stability theory and Pecora-Carroll synchronization criterion, the controller and adaptive rate of these two kinds of synchronization methods are analyzed and designed. Then a new hybrid adaptive projective synchronization method is proposed. Finally, in order to prove the effectiveness of the proposed scheme, the comparison between those controllers is studied by simulation example.

On the dynamics, existence of chaos, control and synchronization of a novel complex chaotic system

In this paper, the authors have studied the dynamics of a novel complex chaotic system with fractional order derivative and found the existence of chaos. The novel complex system is simulated for integer as well as fractional orders which shows some unusual phenomena. The main contribution of this effort is an implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on the fractional Routh–Hurwitz stability conditions and feedback control are given. Also synchronization between a fractional order novel chaotic system and a controlled fractional order novel system using the modified adaptive projective synchronization method for different scaling matrices has been obtained. Numerical simulation results are carried out using the Adams–Bashforth–Moulton method.

Adaptive Complex Projective Synchronization of Chaotic Complex System with disturbance

We define a new synchronization method, adaptive complex projective synchronization, to real synchronization of two chaotic complex systems. The adaptive controller is obtained to make synchronization of two chaotic complex systems based on Lyapunov stability theory. This paper contribution is that make the scale function of projective synchronization is complex numbers. Numerical simulations are presented to illustrate the effectiveness of the proposed synchronization method.

Existence of Chaos, dynamical behaviour with fractional order derivatives and modified adaptive function projective synchronization with uncertain parameters of a chaotic system

In this article, the authors have studied dynamics of Duffing–Van der Pol system with fractional order derivative and found the existence of chaos. The main contribution of this effort is implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on fractional Routh-Hurwitz stability conditions and feedback control are obtained. Also synchronization between fractional order chaotic system and controlled fractional order Duffing–Van der Pol system using modified adaptive function projective synchronization method for different scaling matrix has been obtained. Numerical simulation results which are carried out using Adams–Bashforth–Moulton method show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order systems.

Adaptive projective synchronization for fractional-order T-S fuzzy neural networks with time-delay and uncertain parameters

In this paper, the adaptive projective synchronization of time-delayed fractional-order (FO) T-S fuzzy neural networks is considered. By use of active control and adaptive control method, efficient hybrid control strategies are designed for FO T-S fuzzy neural networks with time-delay and uncertain parameters. Based on the new version of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities, which is easy for checking and applying in practical systems. Finally, numerical simulations have shown to illustrate the effectiveness of the proposed method and the application of the proposed method to secure communications have presented to validate the synchronization method.

Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance

Projective lag synchronization behavior with non-delay and delay coupling in complex dynamical network model is investigated in this paper. Based on Lyapunov stability theory, adaptive control scheme is applied to achieve the projective lag synchronization model with identical, different nodes and even if the delay coupling have constant time delay or time-varying coupling delay. In addition, the model consists of disturbances and fully unknown parameters. Theses parameters are identified by adaptive control and update law. Finally, the simulation results reveal that the states of the dynamical network with non-delay and delay coupling can be asymptotically synchronized onto a desired scaling under the designed controller. Additionally, numerical examples demonstrate the effectiveness of the proposed method.

Adaptive observer-based projective synchronization for chaotic neural networks with mixed time delays

This paper addresses adaptive projective synchronization of chaotic neural networks with mixed time delays based on an observer-based design strategy. For this, the idea of designing nonlinear state observers is used, and a novel adaptive observer-based controller is given to provide projective synchronization between the master and the slave chaotic systems. Lyapunov theorem is also utilized to obtain the adaptation laws for tuning the controller when the parameters of the master system are unknown. The proposed control scheme is successfully applied for projective synchronization of two chaotic neural networks with mixed delays. The simulation results demonstrate the feasibility and efficiency of the presented method.

Adaptive projective lag synchronization of uncertain complex dynamical networks with delay coupling

This paper investigates the problem of projective lag synchronization behavior with delayed coupling in drive-response dynamical networks model with identical and non-identical nodes. An adaptive control method is designed to achieve the projective lag synchronization with constant time delay and with time-varying coupling delay. In addition the model harbors fully unknown parameters and disturbances. By using Lyapunov stability theory and adaptive laws, the unknown parameters are estimated. In addition, the unknown bounded mismatch and disturbance terms are also overcome by the proposed control. Finally, the simulation results reveal that the states of the dynamical network with delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Additionally, the results prove the validity of the proposed method.