Approximating of unstable cycle in nonlinear autonomous systems

Numerical procedures for approximate construction of cycles in nonlinear systems are studied. The procedures are based on functional parameter methods combined with mechanical quadratures, Newtonʹs, and gradient methods. The convergence rate of the procedures is studied, as well as their range of applicability, and their stability with respect to small perturbations of the parameters. The results obtained can be applied to nonlinear problems described by ordinary differential equations, to the systems with delay, and to distributed systems.