Algorithms for searching unstable periodic orbits of chaotic systems
混沌系统不稳定周期轨道的搜索算法

The algorithms for searching unstable periodic orbits (UPO's) of chaotic systems are studied.Firstly,the advantages and disadvantages of the conventional Newton-Raphson algorithm (NR algorithm) and Schmelcher-Diakonos algorithm (SD algorithm) were respectively analyzed.Then,a new searching algorithm called NR-SD algorithm was proposed collecting advantages of both NR and SD algorithms:the global convergence guaranteed,the NR-SD algorithm greatly improves the searching efficiency.Moreover,in the NR-SD algorithm a new strategy of determining initial points was used so that all long-periodic UPO's could be found.Finally,the effectiveness of the NR-SD algorithm was verified by numerical simulation of an example.The relation between the period p and the number of p-periodic UPO's was established as well.