Search for Periodic Solutions of Highly Nonlinear Dynamical Systems

Abstract

Numerical-analytical methods for finding periodic solutions of highly nonlinear autonomous and nonautonomous systems of ordinary differential equations are considered. Algorithms for finding initial conditions corresponding to a periodic solution are proposed. The stability of the found periodic solutions is analyzed using corresponding variational systems. The possibility of studying the evolution of periodic solutions in a strange attractor zone and on its boundaries is discussed, and interactive software implementations of the proposed algorithms are described. Numerical examples are given.