Identical Chaotic Neural Networks Research Articles

Feedback Controller for Identical Synchronization of Chaotic Neural Networks

In this paper, designing an output feedback controller is investigated based on Lyapunov-Krasovkii stability theorem and linear matrix inequality. The goal is to achieve preliminary identical synchronization for synchronizing identical chaotic neural networks. The error convergence of the slave system is the significant advantage of the proposed technique. Also, complete synchronization is achieved with this method clearly. Simulation results of the proposed method for a well- known chaotic neural network show the efficiency of the proposed method.

Anti-synchronization of chaotic neural networks with time-varying delays via linear matrix inequality (LMI)

In this paper, anti-synchronization problem of two identical chaotic neural networks with time-varying delays is proposed. By using time-delay feedback control technique, mean value theorem and the Leibniz-Newton formula, and by constructing appropriately Lyapunov-Krasovskii functional, sufficient condition is proposed to guarantee the asymptotically anti-synchronization of two identical chaotic neural networks. This condition, which is expressed in terms of linear matrix inequality, rely on the connection matrix in the drive and response networks as well as the suitable designed feedback gains in the response network. Finally, the anti-synchronization of two chaotic cellular neural network and Hopfield neural network with time-varying delays are considered to illustrate the effectiveness of the proposed control scheme, in which, when compared with the nonlinear feedback control method, the proposed method shows superior performance. Key words: Lyapunov-Krasovskii functional, chaotic neural networks, anti-synchronization, time-varying delay, linear matrix inequality.

Mean Square Exponential Synchronization of Stochastic Neutral Type Chaotic Neural Networks with Mixed Delay

This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results. Keywords—Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

Synchronization of chaotic neural networks with mixed time delays

In this paper, we investigate the synchronization problems of chaotic neural networks with mixed time delays. We first establish the sufficient conditions for synchronization of identical chaotic neural networks with mixed time delays via linear output feedback control. To overcome the difficulty that complete synchronization between nonidentical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of nonidentical chaotic neural networks with mixed time delays, where the parameters and functions are mismatched. Numerical simulations are carried out to illustrate the main results.

Optimal exponential synchronization of general chaotic delayed neural networks: An LMI approach

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach

In this paper, impulsive control for master–slave synchronization schemes consisting of identical chaotic neural networks is studied. Impulsive control laws are derived based on linear static output feedback. A sufficient condition for global asymptotic synchronization of master–slave chaotic neural networks via output feedback impulsive control is established, in which synchronization is proven in terms of the synchronization errors between the full state vectors. An LMI-based approach for designing linear static output feedback impulsive control laws to globally asymptotically synchronize chaotic neural networks is discussed. With the help of LMI solvers, linear output feedback impulsive controllers can be easily obtained along with the bounds of the impulsive intervals for global asymptotic synchronization. The method is finally illustrated by numerical simulations.

SYNCHRONIZATION IN AN ARRAY OF NONLINEARLY COUPLED CHAOTIC NEURAL NETWORKS WITH DELAY COUPLING

A general complex dynamical network consisting of N nonlinearly coupled identical chaotic neural networks with coupling delays is firstly formulated. Many studied models with coupling systems are special cases of this model. Synchronization in such dynamical network is considered. Based on the Lyapunov–Krasovskii stability theorem, some simple controllers with updated feedback strength are introduced to make the network synchronized. The update gain γi can be properly chosen to make some important nodes synchronized quicker or slower than the rest. Two examples including nearest-neighbor coupled networks and scale-free network are given to verify the validity and effectiveness of the proposed control scheme.

Exponential synchronization of general chaotic delayed neural networks via hybrid feedback

This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, and covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, recurrent multilayer perceptrons (RMLPs). By virtue of Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) technique, some exponential synchronization criteria are derived. Using the drive-response concept, hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria. Finally, detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.

Synchronization of chaotic neural networks via output or state coupling

Abstract We consider the problem of global exponential synchronization between two identical chaotic neural networks that are linearly and unidirectionally coupled. We formulate a general framework for the synchronization problem in which one chaotic neural network, working as the driving system (or master), sends its output or state values to the other, which serves as the response system (or slave). We use Lyapunov functions 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 exponential synchronization regardless of their initial states. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Exponential synchronization of a class of chaotic neural networks

Abstract This paper deals with the synchronization problem of a class of chaotic neural networks with or without delays. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks with or without delays. Using the drive-response concept, a control law is derived to achieve the state synchronization of two identical chaotic neural networks. Furthermore, based on the Lyapunov stability method and the Halanay inequality lemma, a delay independent sufficient exponential synchronization condition is derived. The synchronization condition is easy to verify and relies on the connection matrix in the driven networks and the suitable designed controller gain matrix in the response networks. Finally, some illustrative examples are given to demonstrate the effectiveness of the presented synchronization scheme.