一类三维自治系统的定性和数值研究  

On qualitative analysis and numerical study of a class of 3-D autonomous systems

作　　者：徐登国[1] 赵晓华[1] 

机构地区：[1]云南大学数学系,云南昆明650091

出　　处：《云南大学学报（自然科学版）》2007年第3期223-228,240,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10472100)

摘　　要：讨论了一类含参数的三维自治系统的动力学性质,利用中心流形理论对系统降维,用形式级数法判别出系统平衡点的性质,用数值方法研究了系统的轨线形成蝴蝶形奇怪吸引子的过程,并且分析了系统的耗散性和吸引子的存在性.The dynamical behaviors of a class of 3-D autonomous systems with a parameter are studied. Using center manifold theory, the dimension of the systems is decreased. Property of equilibrium points is achieved by using method of formal series. The formation of butterfly-shaping attracter is studied by using numerical simulation. Moreover, dissipation of the systems and existence of attracter are analyzed.

关 键 词：混沌 平衡点 稳定性 中心流形 吸引子 

分 类 号：O19[理学—数学]