An Analysis Of The Hopf Bifurcation And Computer Simulation For One-dimensional Maxwell-type Nonlinear System

Abstract

One-dimensional nonlinear Maxwell-type system is considered. The initialboundary value problem with mixed type boundary conditions is discussed. It is proved that in some cases of nonlinearity there exists critical value of the boundary data ????, such that for a suffciently small positive values of ?? the steady state solution is linearly stable. But as ?? passes through a critical value ????, the stability changes and a Hopf bifurcation may takes place. The finite difference scheme is constructed. Results of numerical experiments with graphical illustrations are given.