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Volume 7, Number 4, 2017, Pages 1448-1462                                                                DOI:10.11948/2017088
Bifurcation from two equilibria of steady state solutions for non-reversible amplitude equations
Yancong Xu,Rui Xu,Yu Yang
Keywords:Bifurcation, stability, perturbed amplitude equations, eigenvalue problems.
      In this paper, bifurcation and stability of two kinds of constant stationary solutions for non-reversible amplitude equations on a bounded domain with Neumann boundary conditions are investigated by using the perturbation theory and weak nonlinear analysis. The asymptotic behaviors and local properties of two explicit steady state solutions, and pitch-fork bifurcations are also obtained if the bounded domain is regarded as a parameter. In addition, the stability of a new increasing or decaying local steady state solution with oscillations are analyzed.
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