Geodesic
Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 737-743

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Two-frequency parametric resonance in nonlinear dynamical systems is studied by analyzing a delay differential equation with the delay obeying a two-frequency law, which arises in the mathematical simulation of some physical processes. It is shown that the system can exhibit chaotic oscillations (strange attractors) when the parametric excitation frequencies are both close to the doubled eigenfrequency of the system (degenerate case). The formation mechanisms of chaotic attractors are discussed, and the Lyapunov exponents and the Lyapunov dimension are calculated for them. If only one of the parametric excitation frequencies is close to the double eigenfrequency, a two-frequency regime occurs in the system. 
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     title = {Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance},
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A. Yu. Koverga; E. P. Kubyshkin. Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 737-743. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a4/