构造广义Rssler奇怪吸引子的一种新方法

阐述了计算微分方程组最大Lyapunov指数的技术·利用Lyapunov指数作判据,通过坐标变换,构造了一种新的具有旋转对称性的广义Rssler奇怪吸引子,分析了奇怪吸引子的运动特征并计算了奇怪吸引子的关联维数·研究表明:广义Rssler奇怪吸引子是在相空的一个有限区域内,由无穷多个不稳定点集组成的一个集合体,它的几何结构呈现一定程度的自相似性,这是由于它是由广义Rssler方程的反复迭代所引起的“遗传”效应所造成的

New Method Constructing the General Rissler Strange Attractors

The technique of calculating the largest lyapunov exponent of the differential equations was expounded. By utilizing the lyapunov exponent as criterion and transforming the coordinates,a new kind of the rotation symmetry general Rissler strange attractors were constructed,the activitiy characteristic of the strange attractor was analyzed and the correlation dimension of the strange attractors was calculated.The general Rissler strange attractors are a set consisting of unaccountably in finite unstable points inlimit region of the phase space.The heredity effect caused by the repeated iteration of the general Rissler equation give rise to that the geometry structure of the general Rissler strange attractors has some similar property.