Mean almost periodicity and moment exponential stability of semi-discrete random cellular neural networks with fuzzy operations.

Sufang Han,Guoxin Liu,Tianwei Zhang,Jun Ma

doi:10.1371/journal.pone.0220861

Sufang Han, Guoxin Liu + Show 2 more

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https://doi.org/10.1371/journal.pone.0220861

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Abstract

By using the semi-discretization technique of differential equations, the discrete analogue of a kind of cellular neural networks with stochastic perturbations and fuzzy operations is formulated, which gives a more accurate characterization for continuous-time models than that by Euler scheme. Firstly, the existence of at least one p-th mean almost periodic sequence solution of the semi-discrete stochastic models with almost periodic coefficients is investigated by using Minkowski inequality, Hölder inequality and Krasnoselskii’s fixed point theorem. Secondly, the p-th moment global exponential stability of the semi-discrete stochastic models is also studied by using some analytical skills and the proof of contradiction. Finally, a problem of stochastic stabilization for discrete cellular neural networks is studied.

Highlights

Cellular neural networks (CNNs) [1] have been widely applied in psychophysics, parallel computing, perception, robotics associative memory, image processing pattern recognition and combinatorial optimization
There are many scholars focusing on the study of the equilibrium points, periodic solutions and global exponential stability of CNNs with time delays in literatures [2,3,4,5,6,7]
The main contributions of this paper are summed up as: (1) The semi-discrete analogue is established for stochastic fuzzy CNNs (2); (2) A Volterra additive equation is derived for the solution of the semi-discrete stochastic fuzzy CNNs; (3) The existence of p-th mean almost periodic sequence solutions is obtained; (4) A decision theorem is acquired for the p-th moment global exponential stability; (5) A problem of stochastic stabilization for discrete CNNs is proposed and researched

Summary

Introduction

Cellular neural networks (CNNs) [1] have been widely applied in psychophysics, parallel computing, perception, robotics associative memory, image processing pattern recognition and combinatorial optimization. Kong and Fang [50] in 2018 investigated a class of semi-discrete neutral-type neural networks with delays and some results are acquired for the existence of a unique pseudo almost periodic sequence solution which is globally attractive and globally exponentially stable. By using the semi-discretization technique [47], Krasnoselskii’s fixed point theorem and stochastic theory, the main aim of this paper is to establish some decision theorems for the existence of p-th mean almost periodic sequence solutions and p-th moment global exponential stability for the semi-discrete analogue of uncertain system (2). The main contributions of this paper are summed up as: (1) The semi-discrete analogue is established for stochastic fuzzy CNNs (2); (2) A Volterra additive equation is derived for the solution of the semi-discrete stochastic fuzzy CNNs; (3) The existence of p-th mean almost periodic sequence solutions is obtained; (4) A decision theorem is acquired for the p-th moment global exponential stability; (5) A problem of stochastic stabilization for discrete CNNs is proposed and researched. Integrating the above equation from k to t and letting t ! k + 1, we achieve the discrete analogue of system (2) as follows: xiðk þ 1Þ 1⁄4 eÀ aiðkÞxiðkÞ "

À eÀ aiðkÞ Xn

À e0:3 pfifif

Findings

Conclusions and future works