Computing Periodic Orbits of Nonlinear Mappings through Particle Swarm Optimization

Periodic orbits of nonlinear mappings are very useful for the study of dynamical systems. In this paper, a new approach for computing periodic orbits through the global minimization of a properly defined objective function, using the Particle Swarm Optimization method, is introduced. Experimental results on wellknown and widely used nonlinear mappings indicate that the algorithm is robust, it is applicable even in cases where the Newton-family algorithms may not be applicable, and rapid in terms of the time required. Moreover, minor effort is required for the implementation of the proposed approach, and it can, therefore, be considered an efficient alternative for computing periodic orbits of nonlinear mappings.