Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation
The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes a pitchfork bifurcation. The existence (resp.,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/197914 |
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| Summary: | The bifurcation of a
nongeneric homoclinic orbit (i.e., the orbit comes from the
equilibrium along the unstable manifold instead of the center
manifold) connecting a nonhyperbolic equilibrium is
investigated, and the nonhyperbolic equilibrium undergoes a
pitchfork bifurcation. The existence (resp., nonexistence) of a
homoclinic orbit and an 1-periodic orbit are established when the
pitchfork bifurcation does not happen, while as the nonhyperbolic
equilibrium undergoes a pitchfork bifurcation, we obtain the
sufficient conditions for the existence of homoclinic orbit and two
or three heteroclinic orbits, and so forth. Moreover, we explore the
difference between the bifurcation of the nongeneric homoclinic
orbit and the generic one. |
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| ISSN: | 1085-3375 1687-0409 |