Abstract
In this paper, the synchronization problem for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms is investigated under Dirichlet boundary conditions and Neumann boundary conditions, respectively. Based on Lyapunov stability theory, both delay-derivative-dependent and delay-range-dependent conditions are derived in terms of linear matrix inequalities (LMIs), whose solvability heavily depends on the information of reaction-diffusion terms. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. The obtained synchronization results are easy to check and improve upon the existing ones. In our results, the assumptions for the differentiability and monotonicity on the activation functions are removed. It is assumed that the state delay belongs to a given interval, which means that the lower bound of delay is not restricted to be zero. Finally, the feasibility and effectiveness of the proposed methods is shown by simulation examples.
Highlights
In the past several decades, neural networks have been extensively investigated and successfully applied to signal processing, pattern recognition, artificial intelligence, optimization, fault diagnosis, associative memories, and so on
We introduce a linear feedback controller to guarantee the synchronization of generalized reaction-diffusion neural networks with time-varying delays
In [8], the authors studied the asymptotical synchronization in the mean square for reaction-diffusion neural networks with time-varying delays under the Dirichlet boundary conditions
Summary
In the past several decades, neural networks have been extensively investigated and successfully applied to signal processing, pattern recognition, artificial intelligence, optimization, fault diagnosis, associative memories, and so on. In the delaydependent stability analysis, by employing an integral inequality and convex combination technique, some novel delay-dependent stability criteria were derived It has been pointed http://www.mii.lt/NA out that all of these criteria provided a unified frame suitable for both local field neural networks and static neural networks. We consider the problem of synchronization for a class of generalized reaction-diffusion neural networks model with interval time-varying delays under Dirichlet boundary conditions and Neumann boundary conditions, respectively, which includes reaction-diffusion local field neural networks model and the reaction-diffusion static neural networks model. In [14], the authors pointed out that it is quite difficult to find a chaotic attractor for reaction-diffusion delayed neural networks This is an important and interesting open problem. X > Y ), where X and Y are symmetric matrices, means that X − Y is semi-positive definite (resp. positive definite); the shorthand diag(·) denotes the block diagonal matrix; det(·) denotes the determinant of matrix; the symmetric terms in asymmetric matrix are denoted by ∗
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