【摘要】 目的旨在大量生成上半平面极限映射的混沌吸引子及充满Julia集图案.方法分析上半平面极限映射的特点,运用蒙特卡罗搜索法随机搜索参数,通过李雅普诺夫指数判断其动力学特性,构造上半平面极限映射的混沌吸引子及广义充满Julia集.结果运用李雅普诺夫指数测试选定参数下映射的动力学特性,实现了上半平面极限映射的混沌吸引子及广义充满Julia集图案的大量生成.结论根据选定参数下动力系统在动力平面上的轨道特性,可以有效生成上半平面极限映射的混沌吸引子及广义充满Julia集图案.更多还原

【Abstract】 The purpose of this paper is automatically to generate the patterns of chaotic attractors and generalized filled-in Julia sets from mapping with upper halfplane limit and square limit.Monte Carlo method is employed to search the parameter vectors from parameter space of dynamic system of equivalent mapping which is adopted in this paper.Lyapunov exponent is used to judge the characters of the related dynamical system with the parameter vectors which are chosen randomly.In this paper,the calculation of Lyapunov exponent is restricted in the fundamental region,which is a square area.The filled-in Julia sets of the mapping are constructed based on the attracting fields of dynamical system with the parameter vetors which make Lyapunov exponent negative.On the contrary,we choose the parameter vectors which make Lyapunov exponent positive to generate chaotic attractors.In this way,lots of chaotic attractors and filled-in Julia sets from the mappings with upper halflane limit and square limit can be effectively generated.So,abundant dynamical images,which are contained in the related dynamical systems,are developed.更多还原