Plykin-type attractor in nonautonomous coupled oscillators

Abstract

A system of two coupled nonautonomous oscillators is considered. Dynamics of complex amplitudes is governed by differential equations with periodic piecewise continuous dependence of the coefficients on time. The Poincaré map is derived explicitly. With the exclusion of the overall phase, on which the evolution of other variables does not depend, the Poincaré map is reduced to three–dimensional (3D) mapping. It possesses an attractor of Plykin-type located on an invariant sphere. Computer verification of the cone criterion confirms the hyperbolic nature of the attractor in the 3D map. Some results of numerical studies of the dynamics for the coupled oscillators are presented, including the attractor portraits, Lyapunov exponents, and the power spectral density.