| Infinite dimensional dynamical systems play an extremely important role in non-linear science.In the recent years,that lattice systems are a kind of very important In-finite dimensional dynamical systems often occur in a wide variety of applications.So,research asymptotic behavior of solutions for lattice dynamical systems has importantsignificance.Global attractor for lattice dynamical system is a central part in studyinginfinite-dimensional dynamical systems. Since the global attractor sometimes attractsorbits at a relatively slow speed,the exponential attractor is a positively invariant setwhich contains the global attractor and attracts orbits exponentially, we can see that thispaper researches the existence of exponential attractor for one kind of lattice dynami-cal systems.Next,taking into account the system about the time of fractional derivativeforms of existence and uniqueness of solutions.This dissertation is arranged as follows.In chapter1, firstly, the author introducesthe background of one kind of lattice dynamical and the author’research work. At last,the author briefly introduce preliminary results and definition: attractor, exponentialattractor, fractional diferential equations and so on.In chapter2,Considering a kindof lattice dynamical systems,we can prove the existence of exponential attractors forone kind of lattice dynamical systems.In chapter3, Considering the fractional latticesystem, it is proved that the system of the existence and uniqueness of solution. |
