Quasi-periodic solutions and periodic bursters in quasiperiodically driven oscillators |
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Authors: | Faouzi Lakrad Mohamed Belhaq |
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Affiliation: | 1. Yuri Gagarin State Technical University of Saratov, Politehnicheskaya 77, Saratov, 410054, Russian Federation;2. Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russian Federation;3. Saratov State University, Astrakhanskaya, 83, 410012, Russian Federation |
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Abstract: | In this paper, we propose a perturbation method to determine an approximation and conditions of existence of quasi-periodic (QP) solutions and bursting dynamics in a quasi-periodically driven system. The QP forcing consists of two periodic excitations, one with a very slow frequency and the other with a frequency of the same order of the proper frequency of the oscillator. A first averaging is done over the fast dynamics, then the quasi-static solutions of the modulation equations of amplitude and phase are determined and their stability analyzed. We show that a necessary condition for the occurrence of periodic bursters is that the slow excitation is parametric. |
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