Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria
In this chapter we will study global bifurcations corresponding to the appearance of homoclinic or heteroclinic orbits connecting hyperbolic equilibria in continuous-time dynamical systems. We will consider in detail two- and three-dimensional cases for two reasons: first, because in these cases geometrical intuition can be fully exploited, and second, because all the main results can be generalized to higher dimensions.
KeywordsPhase Portrait Invariant Manifold Unstable Manifold Homoclinic Orbit Heteroclinic Orbit
Unable to display preview. Download preview PDF.