Bifurcation Analysis of an amplitude equation

We study the bifurcation and stability of constant stationary solutions (u0, v0) of a particular system of parabolic partial differential equations as amplitude equations on a bounded domain (0, L) with Neumann boundary conditions. In this paper, the asymptotic behavior of the solutions (u0, v0) of the amplitude equations are considered. With the length L of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches are studied. We also analyze the stability of the bifurcated solutions.

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