计算球面对称动力系统Lyapunov指数

通过跟踪球面上相距很近的两个点的球面轨道并计算球面点之间的球内弦长,提出计算球面动力系统轨道的平均Lyapunov指数的计算公式.采用该方法,实现了随机搜索参数并自动计算相应动力系统的Lyapunov指数.当Lyapunov指数大于0时,可得到一个构造球面混沌吸引子的动力系统;当Lyapunov指数小于0时,可得到一个构造球面充满Julia集的动力系统.文中提出的方法可用于随机搜索参数进而生成球面上的对称混沌吸引子和充满Julia集图形.

Computation of Lyapunov Exponents of Dynamic Systems with Spherical Surface Symmetry

For given parameters,a formulary to be used to obtain the Lyapunov exponent on average about a spherical surface dynamic system was provided and was implemented many times by the linear distance between two points instead of computing the curvilinear distance on the sphere surface.For the two points,one was the iterating point omitted transient and the other was very near to the point on the sphere.We were successful to choose parameters randomly and compute the value L of the Lyapunov exponent of the dynamic system corresponding to the parameters.If L>0,we can construct a chaotic dynamic system to create a chaotic attractor;if L<0,we can construct a cycle dynamic system to create a filled-in Julia set.Experiment shows that the method can be used to generate a great number of symmetric chaotic attractors and filled-in Julia sets on the sphere surface.