利用对称性寻找浑沌运动

SEEKING CHAOTIC MOTION BY SYMMETRY

本文研究了一类参数激励和外激励联合作用下的非线性振子,发现其浑沌运动的分布在控制参数平面上具有对称性。

In this paper, we study a class of nonlinear oscillators with parametric and forcing excitation. On the basis of theoretical analysis and digital computer simulation, we first develop a new method of seeking the chaotic solution by symmetry. As this method is able to locate the position of the unknown chaotic point from the position of the known chaotic point on the controlled parametric plane, time of digital computer simulation is greatly reduced. It is shown from an example of this paper that if we find chaotic solution by symmetry digital computer simulation spends only 1/240 of the needed time. Moreover, simulation results reveal that the strange attractor of the known point is symmetrical with regard to origin point with the strange attractor of the axis-symmetry point on the controlled parametric plane.