A new method for global stability analysis of delayed reaction–diffusion neural networks

Fixed-time periodic stabilization of discontinuous reaction-diffusion Cohen-Grossberg neural networks

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.

Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods.

Pinning bipartite synchronization for coupled reaction-diffusion neural networks with antagonistic interactions and switching topologies

In this paper, the bipartite synchronization issue for a class of coupled reaction-diffusion networks with antagonistic interactions and switching topologies is investigated. First of all, by virtue of Lyapunov functional method and pinning control technique, we obtain some sufficient conditions which can guarantee that networks with signed graph topologies realize bipartite synchronization under any initial conditions and arbitrary switching signals. Secondly, for the general switching signal and periodic switching signal, a pinning controller that can ensure bipartite synchronization of reaction-diffusions networks is designed based on the obtained conditions. Meanwhile, a directed relationship between coupling strength and control gains is presented. Thirdly, numerical simulation is provided to demonstrate the correctness and validity of the derived theoretical results for reaction-diffusion systems. We briefly conclude our findings and future work.