中国物理B ›› 2010, Vol. 19 ›› Issue (6): 60510-060510.doi: 10.1088/1674-1056/19/6/060510
李伟义, 张琪昌, 王炜
Li Wei-Yi(李伟义), Zhang Qi-Chang(张琪昌)†, and Wang Wei(王炜)
摘要: Based on the Silnikov criterion, this paper studies a chaotic system of cubic polynomial ordinary differential equations in three dimensions. Using the Cardano formula, it obtains the exact range of the value of the parameter corresponding to chaos by means of the centre manifold theory and the method of multiple scales combined with Floque theory. By calculating the manifold near the equilibrium point, the series expression of the homoclinic orbit is also obtained. The space trajectory and Lyapunov exponent are investigated via numerical simulation, which shows that there is a route to chaos through period-doubling bifurcation and that chaotic attractors exist in the system. The results obtained here mean that chaos occurred in the exact range given in this paper. Numerical simulations also verify the analytical results.
中图分类号: (Numerical simulations of chaotic systems)