caa a22 4500 445361530 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11071-010-9883-3 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9883-3 Global bifurcations and multi-pulse orbits of a parametric excited system with autoparametric resonance [Elektronische Daten] [Hongkui Chen, Qingyu Xu] We consider an autoparametric system which consists of an oscillator coupled with a parametrically excited subsystem. The oscillator and the subsystem are in one-to-one internal resonance. The excited subsystem is in principal parametric resonance. The system contains the most general type of quadratic and cubic non-linearities. The method of second-order averaging is used to yield a set of autonomous equations of the second-order approximations to the parametric excited system with autoparametric resonance. The Shilnikov-type multi-pulse orbits and chaotic dynamics of the averaged equations are studied in detail. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Shilnikov-type multi-pulse homoclinic orbits in the averaged equations. The results obtained above mean the existence of amplitude-modulated chaos in the Smale horseshoe sense in the parametric excited system with autoparametric resonance. The Shilnikov-type multi-pulse chaotic motions of the parametric excited system with autoparametric resonance are also found by using numerical simulation. Springer Science+Business Media B.V., 2010 Global bifurcations nationallicence Autoparametric resonance nationallicence Heteroclinic orbits nationallicence Homoclinic orbits nationallicence Shilnikov-type multi-pulse orbits nationallicence Chen Hongkui College of Science, Chang'an University, 710064, Xi'an, People's Republic of China aut Xu Qingyu Institute of Engineering Mechanics, Xi'an Jiaotong University, 710049, Xi'an, People's Republic of China aut Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 187-216 0924-090X 65:1-2<187 2011 65 11071 https://doi.org/10.1007/s11071-010-9883-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9883-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Hongkui College of Science, Chang'an University, 710064, Xi'an, People's Republic of China aut NATIONALLICENCE 700 1- Xu Qingyu Institute of Engineering Mechanics, Xi'an Jiaotong University, 710049, Xi'an, People's Republic of China aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 187-216 0924-090X 65:1-2<187 2011 65 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer