Almost automorphic solutions in distribution sense for Clifford‐valued stochastic neural network with delays

Abstract

In this paper, a class of Clifford-valued stochastic neural network with delays is investigated, by using a direct method, that is, without decomposing the Clifford-valued system into a real-valued system. Based on the contraction mapping principle and contradiction, sufficient conditions are derived to ensure the existence and stability of almost automorphic solutions for the stochastic networks under consideration. Finally, two numerical examples are provided to show the feasibility of our results.

Multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks with mixed delays

“…What is more, we select 𝜉 A i = (1, 1) T , i = 1, 2; it is followed that matrix ( 17) is an M-matrix, and we can compute which satisfying conditions (22). According to Theorem 2, the model is verified to have [(1 + K 0 ) × (1 + K 1 )] 2 = 16 locally exponentially stable periodic solutions.…”

“…As we know, the applications of real-valued NNs are widely used but only can be employed in a few areas. As an extension of real-valued NNs, complex-valued NNs [13][14][15], quaternion numbers [16,17], and Clifford algebra [18][19][20][21][22] have attracted considerable attention from researchers because of their wide applications. Subramanian and Muthukumar [15], based on linear matrix inequalities, derived the global asymptotic stability conditions, the equilibrium points of the Cohen-Grossberg delayed bidirectional associative memory NN with two types of complex behavior functions.…”

Multipleμ‐stability analysis of time‐varying delayed quaternion‐valued neural networks

“…Therefore, the stability analysis of NNs has attracted much attention of the researchers. [8][9][10][11][12][13][14][15][16][17] When NNs are successfully implemented in associative memory and pattern recognition, the designed system must be stable and possess a large amount of storage capacity. The best way to improve the storage capacity is the increasing the number of stable equilibria of NNs whose state variables are high dimensional.…”

“…For application purposes, the designed NNs are required to be stable. Therefore, the stability analysis of NNs has attracted much attention of the researchers 8–17 …”