38 citations · 99 across the 21 of their papers we have counts for
28 papers
Synchrony and canards in two coupled FitzHugh--Nagumo equations
Bruno F. F. Gonçalves, Isabel S. Labouriau, Alexandre A. P. Rodrigues
We describe the fast-slow dynamics of two FitzHugh--Nagumo equations coupled symmetrically through the slow equations. We use symmetry arguments to find a non-empty open set of par…
Bifurcations and canards in the FitzHugh-Nagumo system: a tutorial in fast-slow dynamics
Bruno F. F. Gonçalves, Isabel S. Labouriau, Alexandre A. P. Rodrigues
In this article, we study the FitzHugh-Nagumo --fast-slow system where the vector fields associated to the slow/fast equations come from the reduction of the Hodgin-Huxley m…
Transitions of bifurcation diagrams of a forced heteroclinic cycle
Isabel S. Labouriau, Alexandre A. P Rodrigues
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of map…
Global planar dynamics with a star node and contracting nolinearity
Begoña Alarcón, Sofia B. S. D. Castro, Isabel S. Labouriau
This is a complete study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a contracting homogeneous po…
High frequency forcing of an attracting heteroclinic cycle
Isabel S. Labouriau, Alexandre A. P. Rodrigues
This article is concerned with the effect of time-periodic forcing on a vector field exhibiting an attracting heteroclinic network. We show that as the forcing frequency tends to i…
Stability of cycles and survival in a Jungle Game with four species
Sofia B. S. D. Castro, Ana M. J. Ferreira, Isabel S. Labouriau
The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic…