Asymptotic Behavior Of Spatially Discrete FitzHugh-Nagumo Equations

FitzHugh-Nagumo system has been widely used in molecular biology and has been paid by many scholars. The thesis mainly considers the FitzHugh-Nagumo lattice system of high dimensional space discretization, and obtains its global at-traction in deterministic environment The existence of the global random attractor is obtained in the environment with white noise. The specific arrangements for this paper are as follows:The first chapter introduces the research background, purpose and signifi-cance of this paper as well as the research status of power system at home and abroad. Some important inequalities are given in this paper.In the second chapter, we prove the existence and upper semicontinuity of the global attractor of the FitzHugh-Nagumo lattice system with high dimension-al space discretization.In the third chapter, we prove the existence of global random attractors for FitzHugh-Nagumo lattice system with high-dimensional space discretization.The fourth chapter is a summary of this article, put forward the problem to be solved.