ArticleBiology2023
Non-Trivial Dynamics in the FizHugh-Rinzel Model and Non-Homogeneous Oscillatory-Excitable Reaction-Diffusions Systems.
Article in Biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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6 authors.
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Abstract
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.
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