Multiple cusp bifurcations

Multiple attractors via CUSP bifurcation in periodically varying environments

Periodically forced (non-autonomous) single species population models support multiple attractors via tangent bifurcations, where the corresponding autonomous models support single attractors. Elaydi and Sacker obtained conditions for the existence of single attractors in periodically forced discrete-time models. In this paper, the Cusp Bifurcation Theorem is used to provide a general framework...

The Cusp Horseshoe and its Bifurcations in the Unfolding of an Inclination-flip Homoclinic Orbit

Unfolding the Cusp-Cusp Bifurcation of Planar Endomorphisms

Abstract. In many applications of practical interest, for example, in control theory, economics, electronics and neural networks, the dynamics of the system under consideration can be modelled by an endomorphism, which is a discrete smooth map that does not have a uniquely defined inverse; one also speaks simply of a noninvertible map. In contrast to the better known case of a dynamical system ...

Resonant homoclinic ip bifurcations

This paper studies three-parameter unfoldings of resonant orbit ip and inclination ip homoclinic orbits. First all known results on codimension-two unfoldings of homoclinic ip bifurcations are presented. Then we show that the orbit ip and inclination ip both feature the creation and destruction of a cusp horseshoe. Furthermore, we show near which resonant ip bifurcations a homoclinic-doubling c...

On Evolute Cusps and Skeleton Bifurcations

Consider a 2D smooth closed curve evolving in time, the skeleton (medial axis) of the figure bounded by the curve, and the evolute of the curve. A new branch of the skeleton can appear / disappear when an evolute cusp intersects the skeleton. In this paper, we describe exact conditions of the skeleton bifurcations corresponding to such intersections. Similar results are also obtained for 3D sur...