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
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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.Abstract: 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.
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