Almost Automorphic Solutions to Cellular Neural Networks With Neutral Type Delays and Leakage Delays on Time Scales

Abstract

In this paper, cellular neural networks (CNNs) with neutral type delays and time-varying leakage delays are investigated. By applying the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, a set of sufficient conditions which ensure the existence and exponential stability of almost automorphic solutions of the model are obtained. An example with its numerical simulations is given to support the theoretical findings.

Exponential convergence in the mean-square sense of nonlocal stochastic almost automorphic genetic regulatory lattice networks

“…A number of processes have a certain regularity; however, they are not completely periodic. So, the study of almost periodic or automorphic sequence has been a significant and interesting topic in the field of difference equations owing to the intensive evolution of the theories of difference equations and the applications in the areas of science and engineering, please refer Li and Shen (2021), Lizama and Mesquita (2013), Aouiti et al (2021), Xu et al (2020a) and Feng and Zong (2018) for some relevant works in this field.…”

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

“…In recent years, the stability, periodicity, almost periodicity, and almost automorphicity of neural networks have been active research fields. In Kong et al, 30 new criteria on periodicity and stabilization of discontinuous uncertain inertial Cohen‐Grossberg neural networks with proportional delays were studied; in Kong et al, 31 delay‐dependent criteria for periodicity and exponential stability of inertial neural networks with time‐varying delays were considered; in Jiang and Wang, 32 the almost periodic solution for quaternion‐valued neural networks with mixed delays on time scales was investigated; in Xu et al, 33 the almost automorphic solution to cellular neural networks with neutral type delays and leakage delays on time scales was researched; in Chen et al, 34 the almost automorphic solution for stochastic differential equations with state‐dependent switching was studied. Inspired by the above, we study the almost automorphic solutions in distribution of Clifford‐valued stochastic neural networks with delays.…”

Permanence and uniform asymptotical stability of a ratio-dependent Leslie system with feedback controls on time scales

“…Later on, the theory of time scales was mainly developed by Bohner and Peterson [17,18]. Recently, the theory of time scales has been applied in neural networks [19], ecological systems [20], as well as a variety of control systems [21]. With the mind of time scale scheme, the above continuous-time system (1) and discretetime system (2) can be unified and integrated.…”