Kuramoto-Sivashinsky方程的稳态解研究

发布时间：2018-03-10 20:24

本文选题：变分法　切入点：Kuramoto-Sivashinsky方程　出处：《科学技术与工程》2017年23期 　论文类型：期刊论文

【摘要】：针对研究Kuramoto-Sivashinsky(K-S)方程的稳态解时遇到的多数轨道快速逃逸困难,应用变分法对该混沌系统的不稳定周期轨道开展了系统计算。当静态K-S方程取很小的积分常数值时,提出利用多尺度平均微扰方法分析对应系统相空间不动点和轨道的分布情况。结果表明,小积分常数值的动力系统行为是极其复杂的,同时存在有多条异宿轨道和周期轨道;当取固定的积分常数c=0.352 1时,可以根据四条周期轨道的拓扑结构建立合适的符号动力学,从而实现对全部短周期轨道的系统搜寻。
[Abstract]:In view of the difficulty of fast escape of most orbits when studying the steady state solution of Kuramoto-Sivashinskyskysky (K-S) equation, the variational method is used to calculate the unstable periodic orbit of the chaotic system. When the static K-S equation takes a very small integral constant value, The multi-scale mean perturbation method is proposed to analyze the distribution of fixed points and orbits in the phase space of the corresponding system. The results show that the dynamic system behavior of small integral constant values is extremely complex, and there are several heteroclinic orbits and periodic orbits at the same time. When the fixed integral constant is 0.352 1, the proper symbolic dynamics can be established according to the topological structure of the four periodic orbits, thus the system search for all the short periodic orbits can be realized.
【作者单位】：中北大学理学院;
【基金】：国家自然科学基金理论物理专项(11647085,11647086) 中北大学2016年校科研基金(XJJ2016036)资助
【分类号】：O19

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