NDLI: Symmetry, cusp bifurcation and chaos of an impact oscillator between two rigid sides

Content Provider	Springer Nature Link
Author	Xie, Jian hua Yue, Yuan
Copyright Year	2007
Abstract	Both the symmetric period n-2 motion and asymmetric one of a one-degree-of-freedom impact oscillator are considered. The theory of bifurcations of the fixed point is applied to such model, and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincaré map. The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmetric ones via pitchfork bifurcation. While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences, and bring about two antisymmetric chaotic attractors subsequently. If the symmetric system is transformed into asymmetric one, bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.
Ending Page	1117
Page Count	9
Starting Page	1109
File Format	PDF
ISSN	02534827
e-ISSN	15732754
Journal	Applied Mathematics and Mechanics
Issue Number	8
Volume Number	28
Language	English
Publisher	Editorial Committee of Applied Mathematics
Publisher Date	2007-01-01
Publisher Place	Hangzhou
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	cusp Poincaré map periodic motion symmetry pitchfork bifurcation Mechanics Bifurcations and instability Applications of Mathematics Mathematical Modeling and Industrial Mathematics chaotic attractor Transition to stochasticity (chaotic behavior)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mechanics of Materials Mechanical Engineering

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