Periodicity of Cohen–Grossberg-type fuzzy neural networks with impulses and time-varying delays

Global polynomial periodicity and polynomial stability of proportional delay Cohen-Grossberg neural networks

This paper tackles the global polynomial periodicity (GPP) and global polynomial stability (GPS) for proportional delay Cohen-Grossberg neural networks (PDCGNNs). By adopting two transformations, designing opportune Lyapunov functionals (LFs) with tunable parameters and taking inequality skills, several delay-dependent criteria of GPP and GPS are acquired for the PDCGNNs. Here the GPP is also a kind of global asymptotic periodicity (GAP), but it has obvious convergence rate and convergence order, and its convergence rate is slower than that of global exponential periodicity (GEP). This is of great significance to the detailed division of periodicity in theory. These acquired criteria are confirmed by a numerical example with four cases. Simultaneously, through the numerical example, the acquired criteria also fully demonstrate their superiority in comparison with existing results. And, in another example, a GPS criterion is used to solve a quadratic programming problem (QPP) to reflect one of the practical applications of the PDCGNNs.

On μ-Pseudo Almost Periodic Solutions for Clifford-Valued Neutral Type Neural Networks With Delays in the Leakage Term

We propose a class of Clifford-valued neutral type neural networks with delays in the leakage term. Using a direct method, that is, without decomposing the Clifford-valued system under consideration into a real-valued system, we obtain sufficient conditions for the existence and global exponential stability of μ -pseudo almost periodic solutions of the Clifford-valued neural network under consideration. Finally, we give a numerical example to show the feasibility of our results.

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

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.