Adaptive almost surely asymptotically synchronization for stochastic delayed neural networks with Markovian switching
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RESEARCH
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Adaptive almost surely asymptotically synchronization for stochastic delayed neural networks with Markovian switching Xiangwu Ding1 , Yan Gao2* , Wuneng Zhou2* , Dongbing Tong2 and Hongye Su3 *
Correspondence: [email protected]; [email protected] 2 College of Information Science and Technology, Donghua University, Shanghai, 201620, P.R. China Full list of author information is available at the end of the article
Abstract In this paper, the problem of the adaptive almost surely asymptotically synchronization for stochastic delayed neural networks with Markovian switching is considered. By utilizing a new nonnegative function and the M-matrix approach, we derive a sufficient condition to ensure adaptive almost surely asymptotically synchronization for stochastic delayed neural networks. Some appropriate parameters analysis and update laws are found via the adaptive feedback control techniques. We also present an illustrative numerical example to demonstrate the effectiveness of the M-matrix-based synchronization condition derived in this paper. Keywords: neutral networks; adaptive almost surely asymptotically synchronization; Markovian switching; stochastic noise; time-varying delays
1 Introduction As we know, the stochastic delayed neural networks (SDNNs) with Markovian switching have played an important role in the fields of science and engineering for their many practical applications, including image processing, pattern recognition, associative memory, and optimization problems [, ]. In the past several decades, the characteristics of the SDNNs with Markovian switching, such as the various stability [, ], have received a lot of attention from scholars in various fields of nonlinear science. Wang et al. in [] considered exponential stability for delayed recurrent neural networks with Markovian jumping parameters. Zhang et al. investigated stochastic stability for Markovian jumping genetic regulatory networks with mixed time delays []. Huang et al. investigated robust stability for stochastic delayed additive neural networks with Markovian switching []. The researchers presented a number of sufficient conditions to achieve the global asymptotic stability and exponential stability for the SDNNs with Markovian switching [–]. As is well known, time delays, as a source of instability and oscillations, always appear in various aspects of neural networks. Recently, the time delays of neural networks have received a lot of attention [–]. The linear matrix inequality (LMI, for short) approach is one of the most extensively used in recent publications [, ]. In recent years, it has been found that the synchronization of the coupled neural networks has potential applications in many fields such as biology and engineering [–]. In the coupled nonlinear dynamical systems, many neural networks may experience abrupt changes in their structure and parameters caused by some phenomena such as compo© 2013 Ding et al.; licensee Springer. This is an Open Access article distributed under the term
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