三阶微分方程模型的混沌性判据  

Chaotic Criterion for Three-Order Differential Equation Model

作　　者：孙丰云[1] 王智峰[1] SUN Feng-yun WANG Zhi-feng(School of Mathematics and Information Sciences, Yantai University, Yantai 264005, Chin)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2016年第4期238-243,共6页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：山东省教育厅基金资助项目(J14LI07)

摘　　要：研究三阶微分方程模型的混沌性判据.研究方法主要采用待定系数法,讨论了三阶微分方程模型的同宿轨、异宿轨的存在性,以及对于不同参数其存在不同意义下的混沌吸引子.在理论分析过程中,结合什尔尼科夫引理验证其有斯梅尔马蹄映射意义下的混沌.Numerical analysis for nonlinear chaotic Lorenz-type System is considered which exhibits different chaot- ic attractors with different eqilibrias for some parameters. The existence of heteroclinic orbits and homoclinic orbits of Sil＇nikov type in a chaotic system is proved by using the undetermined coefficient method. As a result, the Sil＇nikov criterion guarantees that the system has Smale horseshoes.

关 键 词：同宿轨 异宿轨 什尔尼科夫定理 

分 类 号：O175[理学—数学]