Homoclinic bifurcation with nonhyperbolic equilibria
Copyright policy )Homoclinic bifurcation with nonhyperbolic equilibria
The authors study the bifurcation of a homoclinic or heteroclinic orbit with a nonhyperbolic equilibrium, which is a pitchfork bifurcation point. The unperturbed system is assumed to possess a homoclinic orbit \(\Gamma\). Combining two discrete maps in the vicinity of \(\Gamma\), one of which describes the flow close to the equilibrium, while the other one models the dynamics far from equilibrium, it is shown that close to \(\Gamma\) homoclinic or periodic orbits exist.
- East China Normal University China (People's Republic of)
Bifurcation theory for ordinary differential equations, Hyperbolic singular points with homoclinic trajectories in dynamical systems, homoclinic orbit, local coordinate system, periodic orbit, Homoclinic and heteroclinic orbits for dynamical systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, pitchfork bifurcation, Homoclinic and heteroclinic solutions to ordinary differential equations, Poincaré map
Bifurcation theory for ordinary differential equations, Hyperbolic singular points with homoclinic trajectories in dynamical systems, homoclinic orbit, local coordinate system, periodic orbit, Homoclinic and heteroclinic orbits for dynamical systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, pitchfork bifurcation, Homoclinic and heteroclinic solutions to ordinary differential equations, Poincaré map
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