We study a continuous and reversible transition between periodic tonic spiking and bursting activities in a neuron model. It is described as the blue-sky catastrophe, which is a homoclinic bifurcation of a saddle-node periodic orbit of codimension one. This transition constitutes a biophysically plausible mechanism for the regulation of burst duration that increases with no bound like 1/square ...

Grandmont (1985) found that the parameter space of even the simplest, most classical models is stratified into bifurcation regions. But in such classical models all policies are Ricardian equivalent and all solutions are Pareto optimal. As a result he was not able to reach conclusions about policy relevance of his dramatic discovery. Barnett and He (1999,2002) subsequently found transcritical, ...

While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wavelike spatial dependence, either stationary or traveling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation prop...

We study the existence and stability of heteroclinic connections near “hopping” cellular flame patterns. These are dynamic patterns in which individual cells make sequential, and abrupt, changes in their angular positions while they rotate nonuniformly about the center of a circular domain. Normal form analysis and experimental works have shown that these patterns are associated with a homoclin...

We perform both analytical and numerical bifurcation analysis of an alternating forest grassland ecosystem model coupled with human interaction. The consists two nonlinear ordinary differential equations incorporating the perception value forest. system displays multiple steady states corresponding to different densities as well regimes characterized by stable unstable limit cycles. derive anal...

In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known Morsification results for non-isolated singularities and generalise them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects ...