Complex emergent properties in synchronized neuronal oscillations

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

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

This work adresses the dynamics and complexity of the Hindmarsh-Rose neuronal mathematical model. The general aim is the study of the asymptotic behaviour of neuron networks. In this paper, the analysis of these networks uses the synchronization theory via connections between neurons which give rise to emergent properties and self-organization. Our results lead to a classical law which describes many natural or artificial self-organized complex systems. This has been performed using numerical tools.

Mots clés: Hindmarsh-Rose model; synchronization; complexity; emergent properties

Domaines: Systèmes dynamiques [math.DS]

Nathalie Corson, Moulay Aziz-Alaoui. Complex emergent properties in synchronized neuronal oscillations. Springer. From System Complexity to Emergent Properties, Springer - Understanding Complex Systems Series, p. 243, 2009, Understanding Complex Systems Series. ⟨hal-00952594⟩