Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies
In this paper, the dynamics of a system of two coupled van der Pol oscillators is investigated. The coupling between the two oscillators consists of adding to each one’s amplitude a perturbation proportional to the other one. The coupling between two laser oscillators and the coupling between two va...
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| Veröffentlicht in: | Nonlinear dynamics 2014-04, Vol.76 (2), p.1119-1132 |
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| container_title | Nonlinear dynamics |
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| creator | Kengne, J. Chedjou, J. C. Kom, M. Kyamakya, K. Tamba, V. Kamdoum |
| description | In this paper, the dynamics of a system of two coupled van der Pol oscillators is investigated. The coupling between the two oscillators consists of adding to each one’s amplitude a perturbation proportional to the other one. The coupling between two laser oscillators and the coupling between two vacuum tube oscillators are examples of physical/experimental systems related to the model considered in this paper. The stability of fixed points and the symmetries of the model equations are discussed. The bifurcations structures of the system are analyzed with particular attention on the effects of frequency detuning between the two oscillators. It is found that the system exhibits a variety of bifurcations including symmetry breaking, period doubling, and crises when monitoring the frequency detuning parameter in tiny steps. The multistability property of the system for special sets of its parameters is also analyzed. An experimental study of the coupled system is carried out in this work. An appropriate electronic simulator is proposed for the investigations of the dynamic behavior of the system. Correspondences are established between the coefficients of the system model and the components of the electronic circuit. A comparison of experimental and numerical results yields a very good agreement. |
| doi_str_mv | 10.1007/s11071-013-1195-y |
| format | Article |
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C. ; Kom, M. ; Kyamakya, K. ; Tamba, V. Kamdoum</creator><creatorcontrib>Kengne, J. ; Chedjou, J. C. ; Kom, M. ; Kyamakya, K. ; Tamba, V. Kamdoum</creatorcontrib><description>In this paper, the dynamics of a system of two coupled van der Pol oscillators is investigated. The coupling between the two oscillators consists of adding to each one’s amplitude a perturbation proportional to the other one. The coupling between two laser oscillators and the coupling between two vacuum tube oscillators are examples of physical/experimental systems related to the model considered in this paper. The stability of fixed points and the symmetries of the model equations are discussed. The bifurcations structures of the system are analyzed with particular attention on the effects of frequency detuning between the two oscillators. It is found that the system exhibits a variety of bifurcations including symmetry breaking, period doubling, and crises when monitoring the frequency detuning parameter in tiny steps. The multistability property of the system for special sets of its parameters is also analyzed. An experimental study of the coupled system is carried out in this work. An appropriate electronic simulator is proposed for the investigations of the dynamic behavior of the system. Correspondences are established between the coefficients of the system model and the components of the electronic circuit. A comparison of experimental and numerical results yields a very good agreement.</description><identifier>ISSN: 0924-090X</identifier><identifier>EISSN: 1573-269X</identifier><identifier>DOI: 10.1007/s11071-013-1195-y</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Automotive Engineering ; Bifurcations ; Broken symmetry ; Circuits ; Classical Mechanics ; Computer simulation ; Control ; Coupling ; Dynamic tests ; Dynamical Systems ; Dynamics ; Electronic circuits ; Engineering ; Joining ; Mathematical models ; Mechanical Engineering ; Nonlinear dynamics ; Original Paper ; Oscillators ; Parameters ; Period doubling ; Perturbation ; Vacuum tube oscillators ; Vibration</subject><ispartof>Nonlinear dynamics, 2014-04, Vol.76 (2), p.1119-1132</ispartof><rights>Springer Science+Business Media Dordrecht 2014</rights><rights>Nonlinear Dynamics is a copyright of Springer, (2014). 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Kamdoum</creatorcontrib><title>Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies</title><title>Nonlinear dynamics</title><addtitle>Nonlinear Dyn</addtitle><description>In this paper, the dynamics of a system of two coupled van der Pol oscillators is investigated. The coupling between the two oscillators consists of adding to each one’s amplitude a perturbation proportional to the other one. The coupling between two laser oscillators and the coupling between two vacuum tube oscillators are examples of physical/experimental systems related to the model considered in this paper. The stability of fixed points and the symmetries of the model equations are discussed. The bifurcations structures of the system are analyzed with particular attention on the effects of frequency detuning between the two oscillators. It is found that the system exhibits a variety of bifurcations including symmetry breaking, period doubling, and crises when monitoring the frequency detuning parameter in tiny steps. The multistability property of the system for special sets of its parameters is also analyzed. An experimental study of the coupled system is carried out in this work. An appropriate electronic simulator is proposed for the investigations of the dynamic behavior of the system. Correspondences are established between the coefficients of the system model and the components of the electronic circuit. A comparison of experimental and numerical results yields a very good agreement.</description><subject>Automotive Engineering</subject><subject>Bifurcations</subject><subject>Broken symmetry</subject><subject>Circuits</subject><subject>Classical Mechanics</subject><subject>Computer simulation</subject><subject>Control</subject><subject>Coupling</subject><subject>Dynamic tests</subject><subject>Dynamical Systems</subject><subject>Dynamics</subject><subject>Electronic circuits</subject><subject>Engineering</subject><subject>Joining</subject><subject>Mathematical models</subject><subject>Mechanical Engineering</subject><subject>Nonlinear dynamics</subject><subject>Original Paper</subject><subject>Oscillators</subject><subject>Parameters</subject><subject>Period doubling</subject><subject>Perturbation</subject><subject>Vacuum tube oscillators</subject><subject>Vibration</subject><issn>0924-090X</issn><issn>1573-269X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp1kd9qFjEQxYMo-Fl9AO8CvemFazPJZnfTOyn-g4IiCr0L2Wy2Tckmn5ls676Az23qVxQEr4YZfudwhkPIS2CvgbH-FAFYDw0D0QAo2WyPyA5kLxreqcvHZMcUbxum2OVT8gzxhjEmOBt25OcXd7UGk2lC60MwxaeIr6i9NqkOEye6rKF4LGb0wZeN-kgNxQ2LW2iaablL1KZ1H9xEb02kk8v0cwp_7FLGMxrXxWVvTfht6H7s67a4WOoByzp5h8_Jk9kEdC8e5hH59u7t1_MPzcWn9x_P31w0tgVZGgN8Ame6UU1CcDOMwth-HLjg0nI7KSWh7zsFMwjjlOXCjtzOdmSdtG4YenFETg6--5y-rw6LXjxaV5NGl1bU0PUgVataqOjxP-hNWnOs6TTnlZGDbGWl4EDZnBCzm_W-_mbypoHp-2b0oRldm9H3zeitavhBg5WNVy7_df6_6BcNmJPu</recordid><startdate>20140401</startdate><enddate>20140401</enddate><creator>Kengne, J.</creator><creator>Chedjou, J. 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The stability of fixed points and the symmetries of the model equations are discussed. The bifurcations structures of the system are analyzed with particular attention on the effects of frequency detuning between the two oscillators. It is found that the system exhibits a variety of bifurcations including symmetry breaking, period doubling, and crises when monitoring the frequency detuning parameter in tiny steps. The multistability property of the system for special sets of its parameters is also analyzed. An experimental study of the coupled system is carried out in this work. An appropriate electronic simulator is proposed for the investigations of the dynamic behavior of the system. Correspondences are established between the coefficients of the system model and the components of the electronic circuit. 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| subjects | Automotive Engineering Bifurcations Broken symmetry Circuits Classical Mechanics Computer simulation Control Coupling Dynamic tests Dynamical Systems Dynamics Electronic circuits Engineering Joining Mathematical models Mechanical Engineering Nonlinear dynamics Original Paper Oscillators Parameters Period doubling Perturbation Vacuum tube oscillators Vibration |
| title | Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies |
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