Search for Periodic Solutions of Highly Nonlinear Dynamical Systems
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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.
Keywordshighly nonlinear systems of ordinary differential equations periodic solutions stability of periodic solutions strange attractor deterministic chaos
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