作　　者： ; ;

机构地区： 广东工业大学自动化学院

出　　处： 《工程数学学报》 2011年第5期693-701,共9页

摘　　要： 本文用待定系数法证明了具有三次多项式光滑Chua系统异宿轨道的存在性.首先,将光滑Chua系统转换为只含有一个变量的非线性微分方程.其次,证明了该非线性微分方程存在一个指数形式的无穷级数展开式表示的异宿轨道.最后,证明了该无穷级数展开式的一致收敛性,结合Shilnikov不等式,论证了该系统存在Smale马蹄,因而是Shilnikov意义下的混沌. In this paper,the undetermined coefficient method is applied to prove the existence of heteroclinic orbit in a smooth Chua system with a cubic polynomial.Firstly,the smooth Chua system is converted to a nonlinear differential equation with only one variable.Secondly,the nonlinear differential equation is verified to have a heteroclinic orbit expressed by the infinite series expansion with the exponential form.Finally,the uniform convergence of the series expansion of the heteroclinic is proved.Combining the existence of heteroclinic orbit with Shilnikov inequalities,Smale horseshoses has been found in the smooth Chua system,and it is chaotic in the sense of Shilnikov.

关 键 词： 待定系数法 异宿轨道 定理 光滑型 系统

领　　域： [理学] [理学]