arXiv subjects

A. Balti

Publications and source records attributed to A. Balti.

2 recordsLinked to original sources

arXiv2017

Propagation of bursting oscillations in coupled Hodgkin-Huxley Reaction-Diffusion systems

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 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 systems.

math.DS↗

arXiv2015

Computational of periodic oscillations and related bifurcations in the Hodgkin-Huxley model

The Hodgkin-Huxley equations constitute one of the more realistic neuronal models in literature and the most accepted one. It is well known that, depending on the value of the external stimuli current, it exhibits periodic solutions, both stable and unstable. Our aim is to detect and characterize such periodic solutions, exploiting a robust and manageable technique, mainly based on harmonic balance method

math.DS↗