Attractor and synchronization for a complex network of reaction-diffusion systems of FitzHugh-Nagumo type

Ambrosio, Benjamin; Aziz-Alaoui, M. A.; Phan, V L E

doi:10.48550/arxiv.1504.07763

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2017

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Cited by 2 publications

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“…The functions H i represent excitatory nonlinear coupling (i.e. chemical synaptic coupling) between neurons, see [5,6,8,9] and references therein cited. Without loss of generality, we have set the constant C equal to 1.…”

Section: Introductionmentioning

confidence: 99%

Propagation of Bursting Oscillations in Coupled Non-homogeneous Hodgkin–Huxley Reaction–Diffusion Systems

Ambrosio

Aziz-Alaoui

Balti

2017

Differ Equ Dyn Syst

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In this paper, we consider networks of reaction-diffusion systems of Hodgkin-Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as the existence of invariant regions and of the attractor. Then, we illustrate some relevant numerical examples and exhibit bifurcation phenomena and propagation of bursting oscillations through one and two coupled non-homogeneous systems.

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Section: Introductionmentioning

confidence: 99%