Abstract
In this paper, general decay synchronization of delayed bidirectional associative memory neural networks with reaction–diffusion terms is studied. First, a useful lemma is introduced to determine the general decay synchronization of considered systems. Furthermore, a type of nonlinear controller is designed. Then, some sufficient conditions are obtained to insure the general decay synchronization of the drive–response systems via using Lyapunov functional method and Poincaré inequality. Finally, the obtained theoretical results are evaluated by giving one numerical example. The exponential synchronization, polynomial synchronization, and some other types of synchronization can be seen as special cases of the general decay synchronization.
Highlights
In the last two decades, a great number of scholars from science and engineering community have been paying their attention to the investigation of dynamical behavior and control problems of neural networks [1,2,3,4,5,6,7,8,9]
In [15], a nonlinear feedback controller is designed for a general decay synchronization of delayed bidirectional associative memory neural network (BAMNN)
Inspired by the above discussions, in this paper, we are concerned with the general decay synchronization for a BAMNN model with reaction–diffusion terms and time-varying delays
Summary
In the last two decades, a great number of scholars from science and engineering community have been paying their attention to the investigation of dynamical behavior and control problems of neural networks [1,2,3,4,5,6,7,8,9]. In [20], the authors studied the global exponential stability and synchronization of the delayed reaction–diffusion neural networks (RDNNs) under the impulsive control. In [24], the authors have derived sufficient conditions for the H∞ synchronization of RDNNs with mixed time-varying delays based on an adaptive controller method.
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