The Research Of Attractor Bifurcation For Two Classes Of Nonlinear Evolution Equations

This paper consider the attractor bifurcation for two classes of nonlinear evo-lution equations. First of all to provides an analysis of bifurcation to the Chaffee-Infante with Dirichlet boundary condition. That is, assuming that this formula has an odd solution and when the parameter λ throughs the first critical value λ= αλ1, it proves that an attractor is bifurcated. By the theory of attractor bifurcation and Centre Manifold Reduction method, this problem bifurcates an at-tractor which is destructed by the steady state of formula. The second studied the Burgers-Fisher equation. Using Centre Manifold Reduction Method get solution of homogeneous equation bifurcation. In weak external force field εg(x), under the action of perturbation method are used to get the bifurcation perturbation solution of nonhomogeneous equation. The full paper is divided into three partsThe first chapter, mainly introduces the background of Chaffee-Infante equation and Burgers-Fisher equation, centre manifold reduction method, attractor bifurca-tion theory, the perturbation method, and method of innovation.The second chapter, a class of Chaffee-Infante equations of attractor bifurcation.The third chapter, a class of Burgers-Fisher equation of attractor bifurcation.