Chaotic oscillations in a map-based model of neural activity

Maurice Courbage (1) , Vladimir I. Nekorkin (2) , Lev V. Vdovin (2)

1 MSC - Matière et Systèmes Complexes
2 Institute of Applied Physics of RAS

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the phase plane, containing chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking etc.) derived from the proposed model.

Mots clés: Action potential; Membrane potential; Neuron model; FitzHugh-Nagumo model; Dynamical systems; Phase space methods; Vector fields; Vertebrates; Nerve cells

Domaines: Neurosciences [q-bio.NC]; Dynamique Chaotique [nlin.CD]

Maurice Courbage, Vladimir I. Nekorkin, Lev V. Vdovin. Chaotic oscillations in a map-based model of neural activity. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007, 17 (4), pp.043109. ⟨10.1063/1.2795435⟩. ⟨hal-00177949⟩