关键词: 混沌, 周期轨, 迭代算法, 庞加莱截面, 数值计算

Abstract: The periodic orbits provide a skeleton for the organization of complex chaotic systems, for many important characteristics and dynamic properties of these systems can be determined by solving the periodic orbits, such as the accurate calculation of Lyapunov exponents, estimation of topological entropy and description of a chaotic invariant set. First, the paper reviewed the current commonly used four methods to find periodic orbits, which are NR algorithm, Broyden algorithm, SD algorithm and DL algorithm, and analyzed their characteristics and mutual relations. Second, the paper discussed the advantages, disadvantages and scope of each method with specific examples in detail. Finally, the paper pointed out that DL algorithm is more ideal among the four algorithms, and suggested the future research direction.

Key words: chaos, periodic orbit, iterative algorithm, Poincare section, numerical computation