This paper considers a hierarchy of mathematical models of excitable media in one spatial dimension, specifically the FitzHughâ€“Nagumo equation and several models of the dynamics of intracellularâ€¦ (More)

Abstract. The dynamics occurring near a heteroclinic cycle between a hyperbolic equilibrium and a hyperbolic periodic orbit is analyzed. The case of interest is when the equilibrium has aâ€¦ (More)

We present a numerical method for branch switching between homoclinic orbits to equilibria of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method allows us to findâ€¦ (More)

FEDERICO BIZZARRIâˆ—,â€ , DANIELE LINAROâˆ—, BART OLDEMANâ€¡ and MARCO STORACEÂ§ âˆ—Biophysical and Electronic Engineering Department, University of Genoa, Via Opera Pia 11a, Genova, Italy â€ Politecnico diâ€¦ (More)

The saddle-node Hopf bifurcation (SNH) is a generic codimensiontwo bifurcation of equilibria of vector fields in dimension at least three. It has been identified as an organizing centre in numerousâ€¦ (More)

The saddle-node bifurcation on an invariant circle (SNIC) is one of the codimension-one routes to creation or destruction of a periodic orbit in a continuous-time dynamical system. It governs theâ€¦ (More)