113 citations · 292 across the 31 of their papers we have counts for
7 papers · 1 filter
Breaking indecision in multi-agent, multi-option dynamics
Alessio Franci, Martin Golubitsky, Ian Stewart +2
How does a group of agents break indecision when deciding about options with qualities that are hard to distinguish? Biological and artificial multi-agent systems, from honeybees a…
A notion of equivalence for linear complementarity problems with application to the design of non-smooth bifurcations
Fernando Castaños, Félix Miranda-Villatoro, Alessio Franci
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems…
A three-scale model of spatio-temporal bursting
Alessio Franci, Rodolphe Sepulchre
We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits travelin…
Singularly perturbed phase response curves
Pierre Sacré, Alessio Franci
In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (…
Modeling the modulation of neuronal bursting: a singularity theory approach
Alessio Franci, Guillaume Drion, Rodolphe Sepulchre
Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combin…
An organizing center in a planar model of neuronal excitability
Alessio Franci, Guillaume Drion, Rodolphe Sepulchre
The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for th…
A Novel Phase Portrait to Understand Neuronal Excitability
Alessio Franci, Guillaume Drion, Vincent Seutin +1
Fifty years ago, Fitzugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model an…