Global Attractor of Reaction–Diffusion Gene Regulatory Networks with S-Type Delay

Abstract

This paper studies the existence of the global attractor for the reaction–diffusion gene regulatory networks with s-type delay. Firstly, two Hanalay inequalities are proposed and proved, then the uniform boundedness theorem is proved by using these inequalities and semigroup theory and functional analysis technique, the operator splitting technique based on the superposition principle is also utilized to deal with the asymptotic compact of the semigroup. Then some sufficient conditions on existence of global attractor are established, which are easily verifiable and have a wider application range. At last, two examples are discussed to validate the effectiveness of our results. Moreover, the simulation is given by using Matlab.