Non-Trivial Dynamics in the FizHugh–Rinzel Model and Non-Homogeneous Oscillatory-Excitable Reaction-Diffusions Systems
Résumé
This article focuses on the qualitative analysis of complex dynamics arising in a few mathematical models in neuroscience context. We first discuss the dynamics arising in the three-dimensional FitzHugh–Rinzel (FHR) model and then illustrate those arising in a class of non-homogeneous FitzHugh–Nagumo (Nh-FHN) reaction-diffusion systems. FHR and Nh-FHN models can be used to generate relevant complex dynamics and wave-propagation phenomena in neuroscience context. Such complex dynamics include canards, mixed-mode oscillations (MMOs), Hopf-bifurcations and their spatially extended counterpart. Our article highlights original methods to characterize these complex dynamics and how they emerge in ordinary differential equations and spatially extended models.
Mots clés
Ambrosio
B. Aziz-Alaoui
M.A. Mondal
A. Mondal
A. Sharma
S.K. Upadhyay
R.K FitzHugh-Nagumo FitzHugh-Rinzel model fast-slow dynamics bifurcation canard mixed mode oscillations bursting oscillations neuroscience waves
B.
Aziz-Alaoui
M.A.
Mondal
A.
Sharma
S.K.
Upadhyay
R.K FitzHugh-Nagumo
FitzHugh-Rinzel model
fast-slow dynamics
bifurcation
canard
mixed mode oscillations
bursting oscillations
neuroscience
waves
Origine : Publication financée par une institution
Licence : CC BY SA - Paternité - Partage selon les Conditions Initiales
Licence : CC BY SA - Paternité - Partage selon les Conditions Initiales