Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation
Copyright policy )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., 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.
- China University of Geosciences China (People's Republic of)
Bifurcation theory for ordinary differential equations, bifurcation, QA1-939, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, pitchfork bifurcation, Homoclinic and heteroclinic solutions to ordinary differential equations, Mathematics, nongeneric homoclinic orbit
Bifurcation theory for ordinary differential equations, bifurcation, QA1-939, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, pitchfork bifurcation, Homoclinic and heteroclinic solutions to ordinary differential equations, Mathematics, nongeneric homoclinic orbit
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