Stability Analysis in a Class of Markov Switched Stochastic Hopfield Neural Networks

Stabilization of Periodical Discrete Feedback Control for Markov Jumping Stochastic Systems

“…For the inevitable random factor, stochastic neural networks (SNNs, for short) and Markov jumping stochastic neural networks (MJSNNs, for short) are modelled to describe these systems with a random factor, e.g., [30][31][32][33]. The stability issue, as a key property, for SNNs or MJSNNs, has been reported by many researchers in the past, e.g., [34][35][36][37][38][39]. Hence, guaranteeing the stability of SNNs or MJSNNs is dispensable.…”

Almost sure exponential stability of hybrid stochastic delayed Cohen–Grossberg neural networks

“…on t ≥ t 0 and the initial data are (10) has trivial solution x(t) ≡ 0. Consider the corresponding stochastic nondelay Cohen-Grossberg neural network (SCGNN)…”

“…It is known (see, e.g., Zhu et al [22], theorem 3.2 on p. 159) that under Assumptions 3-4, SDCGNN (10) has a unique solution x(t), and we denote the solution by x(t) = x(t 0 , 𝜉, r 0 ). Then, we introduce the following definition.…”

“…Theorem 1. Let Assumptions 1-4 and conditions of Lemma 2 hold, then there exists a positive number 𝜏 * such that the SDCGNN (10) is almost surely exponentially stable when 𝜏 < 𝜏 * . In practice, we can choose 𝛾 ∈ (0, 1) sufficiently small and another free parameter 𝜀 ∈ (0, 1), and let 𝜏 * > 0 be the unique root to the equation…”

“…These mutations mostly cause the system structure or parameter diversity change with variable structure. The Markov switching model [9][10][11] is still further appropriate to describe the variable structure. Moreover, time delays are one of main sources for causing poor performances and instability that frequently occurring in many evolution processes.…”