Finite-time stability analysis of interacting genetic regulatory networks with spatial diffusion term

Abstract

This paper explores the finite-time stable behavior of interacting genetic regulatory networks (GRNs) incorporating spatial diffusion terms under Dirichlet boundary conditions. We propose a coupled model of interacting GRNs and a novel Lyapunov-Krasovskii functional to analyze the dynamic evolution of interactions between the two systems. The lower bound of the time delay can be either zero or non-zero. By employing a delay partitioning approach, we derive less conservative stability criteria for the interacting systems. Finally, numerical simulations are conducted, and the trajectories of mRNA and protein concentrations are provided to validate the accuracy of the proposed criteria.