Algebraic Stability Criteria of Reaction Diffusion Genetic Regulatory Networks With Discrete and Distributed Delays

This paper addresses the stability problem of genetic regulatory networks by involving the spatial diffusion of concentration, discrete and infinite distributed delays. By using the theories of partial differential equation and Lyapunov stability, the global exponential stability criteria in algebraic form are derived for reaction diffusion genetic regulatory networks (RDGRNs) with discrete and distributed delays. The derived stability conditions are simple and can be directly calculated by using the parameters of the networks. Moreover, the theoretical results are universal and can be applied to deal with the stability problem of RDGRNs with or without distributed delays. Eventually, the validity and feasibility of the results are illustrated by numerical simulations.

Automated summary

This paper addresses the stability problem of genetic regulatory networks with reaction diffusion by deriving global exponential stability criteria in algebraic form for networks with discrete and distributed delays. The stability conditions are simple, universal, and can be directly calculated using network parameters. Numerical simulations are used to illustrate the validity and feasibility of the results.