Mean-square exponential input-to-state stability of stochastic inertial neural networks

Wentao Wang,Wei Chen

doi:10.1186/s13662-021-03586-4

Abstract

By introducing some parameters perturbed by white noises, we propose a class of stochastic inertial neural networks in random environments. Constructing two Lyapunov–Krasovskii functionals, we establish the mean-square exponential input-to-state stability on the addressed model, which generalizes and refines the recent results. In addition, an example with numerical simulation is carried out to support the theoretical findings.

Highlights

Babcock and Westervelt [1, 2] have introduced the well-known inertial neural networks that take the following second-order delay differential equations:n xi (t) = –aixi(t) – bixi(t) + cijfj xj(t) j=1 n+ dijgj xj(t – τj) + Ii(t), i ∈ J = {1, 2, . . . , n}, j=1 (1.1)to discover the complicated dynamic behavior of electronic neural networks
The main aim of this paper is to investigate the mean-square exponential input-to-state stability of stochastic inertial neural network (1.4) with initial conditions (1.2)
Motivated by Zhu and Cao [38], who introduced the definition of the mean-square exponential input-to-state stability for stochastic delayed neural networks, together with the mean-square exponential stability (Wang and Chen [43]), we present the following definition

Summary

Introduction

Babcock and Westervelt [1, 2] have introduced the well-known inertial neural networks that take the following second-order delay differential equations:. N xi (t) = –aixi(t) – bixi(t) + cijfj xj(t) j=1 n. + dijgj xj(t – τj) + Ii(t), i ∈ J = {1, 2, . To discover the complicated dynamic behavior of electronic neural networks. The initial conditions are defined as xi(s) = ψi(s), xi(s) = ψi (s), –τ ≤ s ≤ 0, ψi ∈ C1 [–τ , 0], R , i ∈ J, τ = mj∈aJx{τj}, (1.2). Xn(t)) is the state vector, xi (t) is called the ith inertial term, the positive parameters ai, bi, the nonnegative parameters τj, and the other parameters cij, dij are all constant, Ii(t) is the external input of ith neuron at time t and I =.

Objectives

Conclusion