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Creation–annihilation process of limit cycles in the Rayleigh–Duffing oscillator

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Abstract

The present paper examines the creation–annihilation process of limit cycles in the Rayleigh–Duffing oscillator with negative linear damping and negative linear stiffness. It is obtained by the perturbation method, in which the number of limit cycles in the Rayleigh–Duffing oscillator varies with the linear damping and stiffness. Numerical simulations are performed in order to confirm the analytically obtained creation–annihilation process of limit cycles. Moreover, we compare the process of limit cycles in the Rayleigh–Duffing oscillator to that of limit cycles in the van der Pol–Duffing oscillator. The difference in these oscillator is only in nonlinear forces, which causes a qualitative difference in the creation–annihilation processes.

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Acknowledgements

The authors thank Professor Kazuyuki Yagasaki at Niigata University for many useful suggestions and comments on the bifurcation analysis. The present study was supported in part by a Grant-in-Aid for Scientific Research (Scientific Research (B) 22360096) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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  1. Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa, 223-8522, Japan

    Y. Kanai & H. Yabuno

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  1. Y. Kanai
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  2. H. Yabuno
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Correspondence to Y. Kanai.

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Kanai, Y., Yabuno, H. Creation–annihilation process of limit cycles in the Rayleigh–Duffing oscillator. Nonlinear Dyn 70, 1007–1016 (2012). https://doi.org/10.1007/s11071-012-0508-x

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