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ISSN 2542-1905 (Print)

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Hrisanfova S. O., Gubina E. V., Kadina E. J., Kogan L. V., Osipov G. V. The dynamics of two nonlinearly coupled oscillators. Izvestiya VUZ, 2016, vol. 24, iss. 3, pp. 4-20. DOI:

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The dynamics of two nonlinearly coupled oscillators

Hrisanfova Svetlana Olegovna, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Gubina Elena Vasilevna, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Kadina Elena Jurevna, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Kogan Ljudmila Vladimirovna, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Osipov Grigorij Vladimirovich, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"

In this paper the dynamics of two elastically coupled pendulums is studied. The pendulums oscillate under the influence of external rotational moments, their masses are considered to be equal. The current work is motivated by multiple applications in physics and biology that the model has. Due to the fact that most of the previous studies focused on similar systems of higher order, we believe that the current research can serve as a basis for understanding the functioning of more complex oscillatory ensembles. It is, therefore, vital to provide a complete study of the system dynamics for different parameter values. Throughout the study different regimes of the system activity are examined. Thus, non-oscillatory mode, synchronization, periodic and quasi-periodic regimes are discussed in the paper. Synchronization is often considered to be one of the most important forms of interaction between oscillatory elements of various nature. For this reason the synchronization domain is thoroughly investigated in this paper. The main results of the current research are as follow. An analytical approximation of the synchronization domain border is obtained in (d, ?) parameter plane. Here d denotes the coupling strength, whereas ? is the synchronization parameter. By means of numerical integration methods the approximation is also shown to be accurate. In order to provide better understanding of the regimes that exist in the system for various parameter values, bifurcation diagrams for several values of the coupling parameter in in (?1, ?2) plane are drawn.   DOI: 10.18500/0869-6632-2016-24-3-4-20 Paper reference: Khrisanfova S., Kadina E., Gubina E., Kogan L., Osipov G. The dynamics of the two nonlinearly coupled oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24, Issue 3. P. 4–20.   Download full version


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