Periodic orbits of nonlinear mappings play a central role in the study of dynamical systems. Traditional gradientbased algorithms, such as the Newton-family algorithms, have been widely applied for the detection of periodic orbits, through the minimization of a properly defined objective function. However, in the case of discontinuous/nondifferentiable mappings and mappings with poorly behaved partial derivatives, the gradientbased approach is not valid. In such cases, stochastic optimization

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... gorithms have proved to be a valuable tool. In this paper, a new approach for computing periodic orbits through Particle Swarm Optimization, is introduced. The results indicate that the algorithm is robust and efficient. Moreover, the method can be combined with established techniques, such as Deflection, to detect several periodic orbits of a mapping. Finally, the minor effort which is required for the implementation of the proposed approach, renders it an efficient alternative for computing periodic orbits of nonlinear mappings.