Newton-Leipnik系统的慢流形表达式

Slow manifold equation of Newton-Leipnik system

讨论了Newton-Leipnik(N-L)系统的慢流形,利用两种不同的非标准分析方法,分别建立了N-L系统的慢流形方程.将慢流形局部地定义为正交于切丛系统的左快特征向量的平面,利用条件Tzλ1(X).X.=0,导出N-L系统的慢流形方程.并将慢流形看成由两个慢特征向量所生成的曲面,这两个慢特征向量对应J(X)的两个慢变变量特征值λ2(X)和λ3(X),得到N-L系统的慢流形方程.对其轨线的奇异性作了初步定性分析,描述了混沌吸引子的形成过程和系统相轨线动力学行为.

Slow manifold of Newton-Leipnik （ N - L） system is discussed. With two different nonstandard methods, the slow manifold equation of the N - L system is established. Firstly, the slow manifold equation of the nonlinear chaotic dynamics system is obtained by considering that the slow manifold is locally defined by a plane orthogonal to the tangent system＇ s left fast eigenvector. With condition zλ1^T（X）·X = 0, the slow manifold equation of the N - L system is built. Secondly, another method consists of defining the slow manifold as the surface generated by the two slow eigenvectors associated with the two eigenvalues λ2 （X） and λ3 （X） of J（X） , and the slow manifold equation of the N -L system is obtained. Finally, the qualitative behavior and orbits of the system are analyzed. The forming process of the chaos attractor and the dynamic behavior of the system orbits are described.