Construction of Chaotic Attractors with Spherical Symmetries

To automatically generate chaotic attractors with spherical symmetries,a method for computing the Lyapunov exponent of a spherical dynamic system is presented.Given the parameters of a spherical dynamic system,it chooses two points on the sphere,where one is the iterating point and the other is a nearby point on the sphere.Then it tracks these two points and computes their Euclidean distance to obtain the averaged Lyapunov exponent.This method can randomly choose the parameters and get the Lyapunov exponent of the corresponding dynamic system.If the L>0,we can construct a chaotic dynamic system.The experiments showed that the propose method can generate a great number of chaotic attractors with different spherical symmetries.