On the application of optimization methods to the determination of members of families of periodic solutions (Q1420869)

The problem of the computation of periodic solutions of dynamical systems is treated as an unconstrained optimization problem. More specifically, the set of nonlinear equations expressing the periodicity conditions is transformed to an objective function whose minima correspond to the periodic orbits of the considered system. The minimization of this function can be accomplished through any optimization technique. The authors compare their results with some well-known minimization methods for the solution of this problem.