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Complex bursting patterns in Van der Pol system with two slowly changing external forcings

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Abstract

This paper investigates the generation of complex bursting patterns in Van der Pol system with two slowly changing external forcings. Complex bursting patterns, including complex periodic bursting and chaotic bursting, are presented for the cases when the two frequencies are commensurate and incommensurate. These complex bursting patterns are novel and have not been reported in previous work. Based on the fast-slow dynamics, the evolution processes of the slow forcing are presented to reveal the dynamical mechanisms underlying the appearance of these complex bursting patterns. With the change of amplitudes and frequencies, the slow forcing may visit the spiking and rest areas in different ways, which leads to the generation of different complex bursting patterns.

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  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, China

    XiuJing Han & QinSheng Bi

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  1. XiuJing Han
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  2. QinSheng Bi
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Correspondence to QinSheng Bi.

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Han, X., Bi, Q. Complex bursting patterns in Van der Pol system with two slowly changing external forcings. Sci. China Technol. Sci. 55, 702–708 (2012). https://doi.org/10.1007/s11431-011-4655-y

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  • DOI: https://doi.org/10.1007/s11431-011-4655-y

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