Dynamic transitions of the Swift-Hohenberg equation with third-order dispersion

<p style='text-indent:20px;'>The Swift-Hohenberg equation is ubiquitous in the study of bistable dynamics. In this paper, we dynamic transitions with a third-order dispersion term one spacial dimension periodic boundary condition. As control parameter crosses critical value, trivial stable equilibrium solution will lose its stability, and undergoes transition to new physical state, described by local attractor. The main result paper fully characterize type detailed structure using theory [<xref ref-type="bibr" rid="b7">7</xref>]. particular, employing techniques from center manifold theory, reduce infinite dimensional problem finite since space on which exchange stability occurs dimensional. then reduces analysis single or double Hopf bifurcations, completely classify possible phase changes depending for every period.</p>