Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators |
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| Affiliation: | 1. Sede Esmeralda, Universidad de Tarapacá, Av. Luis Emilio Recabarren 2477, Iquique, Chile;2. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile;3. Departamento de Física, Universidad Nacional Experimental Francisco de Miranda, Coro, Venezuela;4. Centro de Nanociencia y Nanotecnologa, CEDENNA, Av. Libertador Bernardo O’Higgins 3363, Santiago, Chile;5. Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco, Chile;6. Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 4873, Santiago, Chile;7. Max Planck Institute for Polymer Research, D 55021 Mainz, Germany;8. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel;1. Trakya University, Faculty of Medicine, Department of Cardiology, Edirne, Turkey;2. Abant Izzet Baysal University, Faculty of Medicine, Department of Cardiology, Bolu, Turkey;3. Yenisehir Hospital, Division of Cardiology, Mersin, Turkey |
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| Abstract: | In this work, we present a novel evidence of the importance of the golden mean criticality of a system of oscillators in agreement with El Naschie’s E-infinity theory. We focus on chaos inhibition in a system of two coupled modified van der Pol oscillators. Depending on the coupling between the two oscillators, the system shows chaotic behavior for different ranges of the coupling parameter. Chaos suppression, as a transition from irregular behavior to a periodical one, is induced by perturbing the system with a harmonic signal with amplitude considerably lower than the value which causes entrainment. The frequency of the perturbation is related to the main frequencies in the spectrum of the freely running system (without perturbation) by the golden mean. We demonstrate that this effect is also obtained for a perturbation with frequency such that the ratio of half the frequency of the first main component in the freely running chaotic spectrum over the frequency of the perturbation is very close (five digits coincidence) to the golden mean. This result is shown to hold for arbitrary values of the coupling parameter in the various ranges of chaotic dynamics of the free running system. |
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