Research On Dynamic Behavior Of Lattice System With Fast Delay

In recent years,many scholars have studied the dynamics of lattice systems,especially the attractor problem.However,in real systems,the internal parameters of the system often change with different time nodes,that is,time is an independent variable and system parameters are dependent variables.This dynamic behavior is called non-autonomous behavior.Since the system will encounter the time delay problem in practical problems,many scholars have considered the long time problem with the time delay affecting the system.However,most of the time delay models studied in the article on the lattice system are with constant time delay or There are very few researches on the attractor problem of lattice systems with fast time delays for derivative-bounded variable time delays.In view of this,there are important theoretical and practical application requirements for the research of non-autonomous systems with fast time delays.The main research work of this article can be summarized as follows:Based on the “tail estimation” method,the equation itself is changed,and the long-term behavior of the solution of the non-autonomous Ginzburg-Landau equation and the nonautonomous Fitz Hugh-Nagumo system with fast time delay is studied.Using the technique of inequality,the sufficient condition for the existence of the attractor of this problem is obtained without requiring the bounded derivative of the time delay term.In addition,study the upper semi-continuity of the attractor when the equation is degenerate.