Abstract
In this paper, the diffusion effect, distributed delays and stochastic disturbance are involved in constructing the model of neural networks. Then, the global exponential synchronization problem is investigated for a class of reaction diffusion neural networks (RDNNs) with infinite distributed delays and stochastic disturbance. By employing the stochastic analysis method and Lyapunov functional theory, an adaptive controller is designed to guarantee the exponential synchronization of the drive and response RDNNs. The derived synchronization conditions are simple and the theoretical results can be directly extended to other RDNNs with or without distributed delays and stochastic disturbance. Finally, one example is provided to verify the effectiveness of the theoretical results and adaptive control approach.
Highlights
During the past several decades, various models of neural networks (NNs) have been put forward and applied in different fields, such as the optimized calculation, associative memory and image processing [1]–[4]
We aim to investigate the drive-response synchronization for reaction diffusion neural networks (RDNNs) with infinite distributed delays and stochastic disturbance
1) This paper addresses the synchronization problem for a class of stochastic RDNNs with infinite distributed delays
Summary
During the past several decades, various models of neural networks (NNs) have been put forward and applied in different fields, such as the optimized calculation, associative memory and image processing [1]–[4] These successful applications are heavily dependent on the dynamical behaviors of NNs, which the main cases are the stability and synchronization. Time delays are inevitable in light of the finite switching limits of neuron amplifiers and the signal transmission [20], [21] They are unavoidably existed in circuits of NNs and may result in undesirable dynamics, such as instability and chaotic behavior [22]–[24]. There is little work on the dynamics of RDNNs with infinite distributed delays and stochastic disturbance, which deserves further investigation and motivates the synchronization study of this paper.
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