Rabinovich-Fabrikant系统的局部分岔  

Local Bifurcation Analysis of the Rabinovich-Fabrikant System

作　　者：黄燮桢 岑金夏 刘永建[3] HUANG Xiezhen;CEN Jinxia;LIU Yongjian(School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, China;School of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, China;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, Guangxi 537000, China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]广西民族大学理学院,广西南宁530006 [3]玉林师范学院广西高校复杂系统优化与大数据处理重点实验室,广西玉林537000

出　　处：《闽南师范大学学报（自然科学版）》2017年第4期10-16,共7页Journal of Minnan Normal University：Natural Science

基　　金：国家自然科学基金(11561069);广西壮族自治区自然科学基金(2015GXNSFAA139002);福建省数学类研究生教育创新基地经费

摘　　要：Rabinovich-Fabrikant(RF)系统由于其强的物理背景而备受关注,同时由于其强非线性,导致对其进行数学分析非常困难.论文通过对系统平衡点局部分岔的精细分析发现,虽然系统只有两个参数,但随参数变化会发生复杂的分岔行为,如广义的鞍结分岔、广义叉型分岔等.借助规范型理论,论文还进一步研究了系统Hopf分岔的数学特征,包括周期解的数学表达式,并借助数值模拟证实了理论分析的正确性.The Rabinovich-Fabrikant(RF)system is a physical system,and it is not an artificial model.At the same time,due to the strong nonlinearity,a rigorous mathematical analysis cannot be performed on it.The RF system is reexamined more closely in this paper.Many new and rich complex dynamics of the system are discovered,which were mostly not reported before,for example the generalized saddle-node bifurcation,the generalized pitchfork bifurcation.Further,based on the normal form theory,complete mathematical characterizations for Hopf bifurcation are rigorously derived and studied.Finally,two complete mathematical characterizations for4D Hopf bifurcation are rigorously derived and studied.Numerical simulations are also performed to justify the theoretical analysis.

关 键 词：RF系统 平衡点 局部分岔 HOPF分岔 

分 类 号：O175[理学—数学]