A novel smooth and discontinuous oscillator with strong irrational nonlinearities

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• 作者：YanWei Han (1)
  QingJie Cao (12) Q.J.Cao@hit.edu.cn
  YuShu Chen (1)
  Marian Wiercigroch (3)
• 关键词：Keywrods irrational nonlinearity &#8211 ; multiple well dynamics &#8211 ; singular closed orbits &#8211 ; Melnikov method
• 刊名：SCIENCE CHINA Physics, Mechanics & Astronomy
• 出版年：2012
• 出版时间：October 2012
• 年：2012
• 卷：55
• 期：10
• 页码：1832-1843
• 全文大小：1.1 MB
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• 作者单位：1. School of Astronautics, Harbin Institute and Technology, Harbin, 150001 China2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043 China3. Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, King鈥檚 College, Aberdeen, AB24 3UE Scotland, UK
• ISSN：1869-1927

文摘

In this paper, we propose a novel nonlinear oscillator with strong irrational nonlinearities having smooth and discontinuous characteristics depending on the values of a smoothness parameter. The oscillator is similar to the SD oscillator, originally introduced in Phys Rev E 69(2006). The equilibrium stability and the complex bifurcations of the unperturbed system are investigated. The bifurcation sets of the equilibria in parameter space are constructed to demonstrate transitions in the multiple well dynamics for both smooth and discontinuous regimes. The Melnikov method is employed to obtain the analytical criteria of chaotic thresholds for the singular closed orbits of homoclinic, homo-heteroclinic, cuspidal heteroclinic and tangent homoclinic orbits of the perturbed system.