本文選題：變分法　切入點：Kuramoto-Sivashinsky方程　出處：《科學技術與工程》2017年23期 　論文類型：期刊論文

【摘要】：針對研究Kuramoto-Sivashinsky(K-S)方程的穩(wěn)態(tài)解時遇到的多數(shù)軌道快速逃逸困難,應用變分法對該混沌系統(tǒng)的不穩(wěn)定周期軌道開展了系統(tǒng)計算。當靜態(tài)K-S方程取很小的積分常數(shù)值時,提出利用多尺度平均微擾方法分析對應系統(tǒng)相空間不動點和軌道的分布情況。結果表明,小積分常數(shù)值的動力系統(tǒng)行為是極其復雜的,同時存在有多條異宿軌道和周期軌道;當取固定的積分常數(shù)c=0.352 1時,可以根據(jù)四條周期軌道的拓撲結構建立合適的符號動力學,從而實現(xiàn)對全部短周期軌道的系統(tǒng)搜尋。
[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.
【作者單位】： 中北大學理學院;
【基金】：國家自然科學基金理論物理專項(11647085,11647086) 中北大學2016年�？蒲谢�(XJJ2016036)資助
【分類號】：O19

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