混沌系统周期轨道的最速下降方法研究

A new method of searching for unstable periodic solutions in a chaotic system is presented in this paper. The Taylor expansion is applied to transform a differential dynamical system to a discrete dynamical system. A target function is then built such that its minimum (0 value) corresponds to an unstable periodic orbit for the differential system. A searching method for pseudo-periodic orbits is given to determine the initial value for an optimization method. The steepest descent method is then employed to find the minimum of the target function. This method is applied to the famous Lorenz system and the unstable periodic orbits obtained include a simple cycle, a super cycle and a double cycle. The results show that this method is effective and practical.