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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Nonlinear Dynamicsarrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Nonlinear Dynamics
Article . 2012 . Peer-reviewed
License: Springer TDM
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Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation

Authors: Yancong Xu; Yancong Xu; Fengjie Geng;

Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation

Abstract

In this paper, using the local coordinate moving frame approach, we investigate bifurcations of generic heteroclinic loop with a hyperbolic equilibrium and a nonhyperbolic equilibrium which undergoes a pitchfork bifurcation. Under some generic hypotheses, the existence of homoclinic loop, heteroclinic loop, periodic orbit and three or four heteroclinic orbits is obtained. In addition, the non-coexistence conditions for homoclinic loop and periodic orbit are also given. Note that the results achieved here can be extended to higher dimensional systems.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
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