Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays

Abstract

This article investigates the passivity of reaction–diffusion genetic regulatory networks (GRNs) with time-varying delays and uncertainty terms under Dirichlet, Neumann, and Robin boundary conditions. We provide delay-dependent stability criteria by constructing appropriate Lyapunov–Krasovskii functions and linear matrix inequalities, and offer conditions sufficient to ensure the passivity of GRNs. We conducted a comparative analysis of GRNs under these three conditions. Numerical examples of the proposed approaches are provided to illustrate its effectiveness, and represent the three-dimensional figures of the trajectories of the concentrations of mRNA and the proteins of GRNs under Dirichlet boundary conditions.