Dynamical Behavior Of Two Lattice Chemical Reaction Equations

Dynamical system is an important part of nonlinear science, itstudies the global qualitative behavior of the evolution system. Lat-tice dynamical system is one of the important and difcult contentsin studying the infnite dimensional dynamical system. So far, thereare series of results on the asymptotic behavior of lattice dynamicalsystem.This paper mainly studies the autonomous lattice three compo-nent reversible Gray-Scott equations and the non-autonomous latticeSelkov equations. It is arranged as follows.In Chapter2, we study the asymptotic behavior of solution forthe autonomous lattice three component reversible Gray-Scott equa-tions. First, we prove the existence of the global attractor for thesemigroup generated by the solution operators associated to the lat-tice Gray-Scott equations. Then we give an upper bound of the Kol-mogorov-entropy for the global attractor.In Chapter3, we consider the asymptotic behavior of solutionfor the non-autonomous lattice Selkov equations. We frst prove theexistence of the uniform attractor for the process generated by thesolution operators associated to the lattice Selkov equations. Thenwe give an upper bound of the Kolmogorov-entropy for the uniformattractor. Finally, we verify the upper semicontinuity of the uniformattractor, using the fnite lattice systems to approximate the infnitelattice system.Chapter4is the summary of the paper.