Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling

This paper investigates the adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling, in which the weights of links between two connected nodes are time varying. By the stability analysis of the impulsive functional differential equation, the sufficient conditions for achieving projective synchronization are obtained, and a hybrid controller, that is, an adaptive feedback controller with impulsive control effects is designed. The numerical examples are presented to illustrate the effectiveness and advantage of the proposed synchronization criteria.     

Projective synchronization in a driven-response dynamical network with coupling time-varying delay

This paper studies the projective synchronization in a driven-response dynamical network with coupling time-varying delay model via impulsive control, in which the weights of links are time varying. Based on the stability analysis of the impulsive functional differential equations, some sufficient conditions for the projective synchronization are derived. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results.     

Finite-time synchronization for complex dynamical networks with time-varying delays

The finite-time synchronization problem of a class of complex dynamical networks with time-varying delays is addressed in this paper. The network topology is assumed to be directed and weakly connected. By introducing a special zero row-sum matrix and combining the Lyapunov?CKrasovskii functional method and the Kronecker product technique, a sufficient condition is presented, which consist of two simple low-dimensional matrix inequalities. Illustrative example is given to show the feasibility of the proposed method.     

Adaptive projective synchronization of dynamical networks with distributed time delays

In this paper, the adaptive projective synchronization of dynamical network with distributed time delays is investigated. Network with unknown topology and network with both unknown topology and system parameters of node dynamics are considered respectively. Based on Lyapunov stability theory and LaSalle’s invariance principle, the sufficient conditions for achieving projective synchronization are obtained. Numerical examples are provided to show the effectiveness of the proposed method.     

Synchronization in complex dynamical networks with interval time-varying coupling delays

This paper deals with the synchronization problem of complex dynamical networks with interval time-varying coupling delays. A simple local linear feedback controller is introduced to guarantee the synchronizability of the networks. Some delay-dependent synchronization conditions for the controlled complex dynamical networks are presented by using the Lyapunov–Krasovskii functional method and the reciprocally convex combination approach. Theoretical analysis and numerical examples show that the obtained conditions have less computational complexity and less conservatism than some recently reported ones.     

Function projective synchronization of impulsive neural networks with mixed time-varying delays

In this paper, the exponential function projective synchronization of impulsive neural networks with mixed time-varying delays is investigated. Based on the contradiction method and analysis technique, some novel criteria are obtained to guarantee the function projective synchronization of considered networks via combining open-loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization, and the stabilization of the addressed neural networks. Finally, two examples and their numerical simulations are given to show the effectiveness and feasibility of the proposed synchronization schemes.     

Projective-dual synchronization in delay dynamical systems with time-varying coupling delay

The existence of projective-dual-anticipating, projective-dual, and projective-dual-lag synchronization in a coupled time-delayed systems with modulated delay time is investigated via nonlinear observer design approach. Transition from projective-dual-anticipating to projective-dual synchronization and from projective-dual to projective-dual-lag synchronization as a function of variable coupling delay τ _p (t) is discussed. Using Krasovskii–Lyapunov stability theory, a general condition for projective-dual synchronization is derived. Numerical simulations on the chaotic Ikeda and Mackey–Glass systems are given to demonstrate the effectiveness of the theoretical results.     

Synchronization of neutral complex dynamical networks with coupling time-varying delays

In this paper, the synchronization problem for a class of neutral complex dynamical networks with coupling time-varying delays is considered. A delay-dependent synchronization criterion is derived for the synchronization of neutral complex dynamical networks. By the use of a convex representation of the sector-restricted nonlinearity in system dynamics, the stability condition based on the discretized Lyapunov?CKrasovskii functional is obtained via LMI (linear matrix inequality) formulation. The effectiveness of our work is verified through a numerical example and simulation.     

Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems

In drive-response complex-variable systems, projective synchronization with respect to a real number, real matrix, or even real function means that drive-response systems evolve simultaneously along the same or inverse direction in a complex plane. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, this paper investigates projective synchronization in drive-response networks of coupled complex-variable chaotic systems with respect to complex numbers, called complex projective synchronization (CPS). The adaptive feedback control method is adopted first to achieve CPS in a general drive-response network. For a special class of drive-response networks, the CPS is achieved via pinning control. Furthermore, a universal pinning control scheme is proposed via the adaptive coupling strength method, several simple and useful criteria for CPS are obtained, and all results are illustrated by numerical examples.     

Finite-time synchronization for complex dynamical networks with hybrid coupling and time-varying delay

In this paper, the finite-time synchronization problem has been investigated for a general array model of dynamical networks with time-varying delay and hybrid coupling. The Lyapunov functional method and linear matrix inequality technique are employed to obtain some synchronization criteria less-conservative and delay-dependent. Here, the coupling configuration matrices are not required to be symmetric or irreducible, neither is their off-diagonal entries assumed to be nonnegative. Moreover, the inner linking matrices are arbitrary real matrices. Finally, numerical examples are given to demonstrate the effectiveness of the proposed synchronous criteria.     

Global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays

This paper is concerned with the global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays in the presence of disturbances. Firstly, the property with respect to the global stability in fixed time is developed for semi-Markovian switching nonlinear systems. Subsequently, a novel sliding manifold with double integration is presented based on the proposed principle of convergence in fixed time. Under the designed sliding mode controller, the state trajectory of synchronization error system is driven to the prescribed sliding manifold in fixed time. In addition, the global stability in fixed time of sliding mode dynamics is proved analytically. By means of the stochastic Lyapunov–Krasovskii functional approach, the synchronization condition is established in terms of linear matrix inequalities; moreover, the stochastic fixed settling-time can be determined to any desired values in advance, via the configuration of parameters in the proposed controller. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results and the feasibility of the proposed approach.

     

Adaptive event-triggered prescribed performance learning synchronization for complex dynamical networks with unknown time-varying coupling strength

Nonlinear Dynamics - In this paper, we focus on investigating the prescribed performance synchronization problems of complex dynamical networks with unknown time-varying coupling strength by...     

Adaptive generalized function matrix projective lag synchronization of uncertain complex dynamical networks with different dimensions

Generalized function matrix projective lag synchronization of uncertain complex dynamical networks with different dimension of nodes via adaptive control method is investigated in this paper. Based on Lyapunov stability theory, adaptive controller is obtained and unknown parameters of both the drive network and the response network are estimated by adaptive laws. In addition, the three-dimension chaotic system and the four-dimension hyperchaotic system, respectively, as the nodes of the drive and response network are analyzed in detail, and numerical simulation results are presented to illustrate the effectiveness of the theoretical results.     

Complex projective synchronization in coupled chaotic complex dynamical systems

In previous papers, the projective factors are always chosen as real numbers, real matrices, or even real-valued functions, which means the coupled systems evolve in the same or inverse direction simultaneously. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, the projective synchronization with respect to a complex factor, called complex projective synchronization (CPS), should be taken into consideration. In this paper, based on Lyapunov stability theory, three typical chaotic complex dynamical systems are considered and the corresponding controllers are designed to achieve the complex projective synchronization. Further, an adaptive control method is adopted to design a universal controller for partially linear systems. Numerical examples are provided to show the effectiveness of the proposed method.     

Exponential synchronization for second-order nonlinear systems in complex dynamical networks with time-varying inner coupling via distributed event-triggered transmission strategy

This paper focuses on the exponential synchronization problem of complex dynamical networks (CDNs) with time-varying inner coupling via distributed event-triggered transmission strategy. Information update is driven by properly defined event, which depends on the measurement error. Each node is described as a second-order nonlinear dynamic system and only exchanges information with its neighboring nodes over a directed network. Suppose that the network communication topology contains a directed spanning tree. A sufficient condition for achieving exponential synchronization of second-order nonlinear systems in CDNs with time-varying inner coupling is derived. Detailed theoretical analysis on exponential synchronization is performed by the virtues of algebraic graph theory, distributed event-triggered transmission strategy, matrix inequality and the special Lyapunov stability analysis method. Moreover, the Zeno behavior is excluded as well by the strictly positive sampling intervals based on the upper right-hand Dini derivative. It is noted that the amount of communication among network nodes and network congestion have been significantly reduced so as to avoid the waste of network resources. Finally, a simulation example is given to show the effectiveness of the proposed exponential synchronization criteria.