A novel smooth and discontinuous oscillator with strong irrational nonlinearities  

作　　者：HAN YanWei CAO QingJie CHEN YuShu WIERCIGROCH Marian 

机构地区：[1]School of Astronautics,Harbin Institute and Technology,Harbin 150001,China [2]Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China [3]Centre for Applied Dynamics Research,School of Engineering,University of Aberdeen,King's College,Aberdeen AB243UE,Scotland,UK

出　　处：《Science China(Physics,Mechanics & Astronomy)》2012年第10期1832-1843,共12页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10872136,11072065 and 10932006)

摘　　要：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.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.

关 键 词：irrational nonlinearity multiple well dynamics singular closed orbits Melnikov method 

分 类 号：O322[理学—一般力学与力学基础] TP273[理学—力学]