Couplages de neurones de type Hindmarsh-Rose : de la synchronisation à l'émergence de propriétés

Nathalie Corson (1) , Moulay Aziz-Alaoui (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

The Hodgkin-Huxley mathematical neuron model describes the neuron behaviour in terms of ionic kinetics across the membrane. The Hindmarsh-Rose differential slow-fast system, based on the Hodgkin-Huxley one, models the flux of information through the neuron. Interactions between neurons are possible thanks to synapses, which can be represented by a linear coupling function (electrical synapses) or by a nonlinear with threshold coupling function (chemical synapses). After a short presentation of the asymptotic dynamics of the Hindmarsh-Rose system, we numerically study the coupling strength which is necessary to observe synchronisation between neurons. This work has been done in both cases of linear coupling and of nonlinear coupling of several neurons. Each neuron is supposed to be connected to all the others. First, all the neurons are identical and then, we make the parameters vary so that all neurons are slightly different from one another. Interactions (linear or not) between the elements (identical or not) of this system give birth to some new properties related to the coupling strength necessary to have a synchronization phenomenon between $n$ neurons. These emergent properties are given by heuristic laws which are specific to complex systems.

Domaines: Systèmes dynamiques [math.DS]

Nathalie Corson, Moulay Aziz-Alaoui. Couplages de neurones de type Hindmarsh-Rose : de la synchronisation à l'émergence de propriétés. 12e Rencontre du Non-Linéaire Paris 2009, Mar 2009, Paris, France. p. 47. ⟨hal-00952570⟩