Subharmonic and grazing bifurcations for a simple bilinear oscillator |
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| Institution: | 1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China;2. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China;1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;2. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China;3. Institute for Complex Systems and Mathematical Biology King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom |
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| Abstract: | In this paper, subharmonic and grazing bifurcations for a simple bilinear oscillator, namely the limit discontinuous case of the smooth and discontinuous (SD) oscillator are studied. This system is an important model that can be used to investigate the transition from smooth to discontinuous dynamics. A combination of analytical and numerical methods is used to investigate the existence, stability and bifurcations of symmetric and asymmetric subharmonic orbits. Grazing bifurcations for a particular periodic orbit are also discussed and numerical results suggest that the bifurcations are discontinuous. We show via concrete numerical experiments that the dynamics of the system for the case of large dissipation is quite different from that for the case of small dissipation. |
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| Keywords: | SD oscillator Piecewise linear system Subharmonic orbit Grazing bifurcation Chaos |
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