Abstract: 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 ...