| Bifurcation and Chaos in a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation |
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| 作者姓名： | Wei Li Peng-cheng XuInstitute of Mathematics Beijing University of Chemical Technology Beijing ChinaInstitute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China |
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| 作者单位： | Wei Li，Peng-cheng XuInstitute of Mathematics，Beijing University of Chemical Technology，Beijing 100029，ChinaInstitute of Applied Mathematics，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | the National Key Basic Research Special Fund (No.G.1998020307). |
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| 摘 要： | In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis.
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Bifurcation and Chaos in a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation |
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| Wei Li,Peng-cheng XuInstitute of Mathematics,Beijing University of Chemical Technology,Beijing ,ChinaInstitute of Applied Mathematics,Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing ,China.Bifurcation and Chaos in a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation[J].Acta Mathematicae Applicatae Sinica,2002,18(3):501-512. |
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| Authors: | Wei Li Peng-cheng Xu |
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| Institution: | (1) Institute of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China (E-mail: Liwei_buct@sohu.net), CN;(2) Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing 100080, China, CN |
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| Abstract: | In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis. |
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| Keywords: | Bifurcation chaos transversal homoclinic orbit |
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