Finite‐time stability of reaction–diffusion genetic regulatory networks with nondifferential time‐varying mixed delays

Abstract

This paper explores the finite‐time stability of reaction–diffusion genetic regulatory networks with time‐varying mixed delays. These delays encompass discrete delays and distributed delays. Unlike many existing studies, this paper assumes that both types of delays are bounded and continuous, without requiring differentiability. Additionally, the analysis combines the inequality approach and comparison method, while neither a Lyapunov–Krasovskii functional is constructed nor the finite‐time stability theorem is involved. The finite‐time stability of the addressed networks is then ensured by several suitable algebraic criteria. Some extended results are deduced for networks without considering reaction–diffusion and distributed delays effects as special cases. Finally, the validness of the derived results is proved by numerical simulations.