Abstract
In this paper, we devote to the investigation of passivity in two types of coupled stochastic neural networks (CSNNs) with multiweights and incompatible input and output dimensions. First, some new definitions of passivity are proposed for stochastic systems that may have incompatible input and output dimensions. By utilizing stochastic analysis techniques and Lyapunov functional method, several sufficient conditions are respectively developed for ensuring that CSNNs without and with multiple delay couplings can realize passivity. Besides, the synchronization criteria for CSNNs with multiweights are established by employing the results of output-strictly passivity. Finally, two simulation examples are given to illustrate the validity of the theoretical results.
Highlights
In recent decades, neural networks (NNs) have potential applications in the image encryption, pseudorandom number generators, optimization, and other areas [1,2,3], which depend on the dynamical behaviors of NNs including stability and passivity. erefore, the stability [4,5,6,7,8] and passivity [9,10,11,12,13,14] for various NNs have received special attention in recent years
As it is known to all, stochastic perturbations are unavoidable in the implementation of NNs and may cause undesirable dynamical behaviors in NNs [15, 16]. erefore, the dynamical behaviors including the stability [17,18,19,20,21] and passivity [22,23,24,25,26,27] have been widely investigated by numerous researchers for NNs with stochastic perturbations in recent years
Some sufficient conditions to ensure the passivity of multiweighted CSNNs (MWCSNNs) are obtained by taking advantage of the Lyapunov functional method and stochastic analysis techniques, and a synchronization criterion is developed by utilizing the result of output-strictly passivity. ird, we further address the passivity and synchronization for coupled stochastic neural networks (CSNNs) with multiple delay couplings (CSNNMDCs)
Summary
Neural networks (NNs) have potential applications in the image encryption, pseudorandom number generators, optimization, and other areas [1,2,3], which depend on the dynamical behaviors of NNs including stability and passivity. erefore, the stability [4,5,6,7,8] and passivity [9,10,11,12,13,14] for various NNs have received special attention in recent years. In [24], the authors took into account one type of uncertain SNNs with distributed and discrete time-varying delays and gave some passivity criteria with the help of integral inequality technique. Nagamani et al [25], respectively, discussed the passivity and dissipativity for Markovian jump stochastic NNs with two types of time-varying delays and obtained several delay-dependent passivity and dissipativity criteria by taking a suitable Lyapunov functional. Some sufficient conditions to ensure the passivity of MWCSNNs are obtained by taking advantage of the Lyapunov functional method and stochastic analysis techniques, and a synchronization criterion is developed by utilizing the result of output-strictly passivity.
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