论文标题
带有三阶分散的Swift-Hohenberg方程的动态过渡
Dynamic Transitions of the Swift-Hohenberg Equation with Third-Order Dispersion
论文作者
论文摘要
Swift-Hohenberg方程在可动力学的研究中无处不在。在本文中，我们研究了具有周期性边界条件的一个空间维度的三阶分散项的Swift-Hohenberg方程的动态过渡。当控制参数越过临界值时，微不足道的稳定平衡解决方案将失去其稳定性，并经历了由局部吸引子描述的新物理状态的动态过渡。本文的主要结果是使用动态过渡理论充分表征过渡的类型和详细结构。特别是，采用中心歧管理论的技术，我们将这个无限的维度问题减少到有限问题，因为发生稳定交换的空间是有限的维度。然后，该问题减少了单个或双HOPF分叉的分析，我们根据每个空间时期的分散体完全对可能的阶段变化进行了分类。
The Swift-Hohenberg equation is ubiquitous in the study of bistable dynamics. In this paper, we study the dynamic transitions of the Swift-Hohenberg equation with a third-order dispersion term in one spacial dimension with a periodic boundary condition. As a control parameter crosses a critical value, the trivial stable equilibrium solution will lose its stability, and undergoes a dynamic transition to a new physical state, described by a local attractor. The main result of this paper is to fully characterize the type and detailed structure of the transition using dynamic transition theory. In particular, employing techniques from center manifold theory, we reduce this infinite dimensional problem to a finite one since the space on which the exchange of stability occurs is finite dimensional. The problem then reduces to analysis of single or double Hopf bifurcations, and we completely classify the possible phase changes depending on the dispersion for every spacial period.
