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.
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Original Russian Text © L.F. Petrov, 2018, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2018, Vol. 58, No. 3, pp. 403–413.
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Petrov, L.F. Search for Periodic Solutions of Highly Nonlinear Dynamical Systems. Comput. Math. and Math. Phys. 58, 384–393 (2018). https://doi.org/10.1134/S0965542518030089
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DOI: https://doi.org/10.1134/S0965542518030089