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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- 2.The Duffing Equation: Nonlinear Oscillators and Their Behavior, Ed. by I. Kovacic and M. J. Brennan (Wiley, Chichester, 2011).Google Scholar
- 4.B. I. Kryukov, Forced Oscillations of Essentially Nonlinear Systems (Mashinostroenie, Moscow, 1984) [in Russian].Google Scholar
- 6.L. F. Petrov, Methods for Dynamic Economic Analysis (Infra-M, Moscow, 2010) [in Russian].Google Scholar
- 12.L. F. Petrov, “Interactive computational search strategy of periodic solutions in essentially nonlinear dynamics,” Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, Ed. by M. G. Cojocaru (Springer International, Switzerland, 2015), pp. 355–360. doi 10.1007/978-3-319-12307-3_51CrossRefGoogle Scholar
- 13.A. Yu. Gornov, Computational Techniques for Solving Optimal Control Problems (Nauka, Novosibirsk, 2009) [in Russian].Google Scholar
- 14.A. B. Dorzhieva and L. F. Petrov, “Numerical study of limit cycles of a dynamical system using the OPTCONA software code,” Proceedings of Lyapunov Conference 2012 (2012), pp. 14.Google Scholar