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Abstract: A system of two coupled non-autonomous oscillators is considered. Dynamics ofcomplex amplitudes is governed by differential equations with periodicpiecewise continuous dependence of the coefficients on time. The Poincar\-{e}map is derived explicitly. With exclusion of the overall phase, on which theevolution of other variables does not depend, the Poincar\-{e} map is reducedto 3D mapping. It possesses an attractor of Plykin type located on an invariantsphere. Computer verification of the cone criterion confirms the hyperbolicnature of the attractor in the 3D map. Some results of numerical studies of thedynamics for the coupled oscillators are presented, including the attractorportraits, Lyapunov exponents, and the power spectral density.



Author: Sergey P. Kuznetsov

Source: https://arxiv.org/







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