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Nekorkin V. I., Vdovin L. V. Map-based model of the neural activity. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 5, pp. 36-60. DOI: 10.18500/0869-6632-2007-15-5-36-60

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Map-based model of the neural activity

Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences
Vdovin Lev Vjacheslavovich, Institute of Applied Physics of the Russian Academy of Sciences

A two-dimensional model exhibiting the chaotic spiking-bursting activity of real neurons is proposed. The model is given by the discontinuous two-dimensional map. It is constructed on the basis of the discrete modification of the FitzHugh–Nagumo model and one-dimensional Lorenz-type map. We have studied the dynamics of the system, found the conditions on the parameters under which chaotic attractor exists. The structure and properties of the attractor is studied. This attractor mimics spiking-bursting oscillations. We have also showed that map is applicable for simulation of other regimes of neural oscillatory activity such as subthreshold oscillations and periodic and chaotic spiking or it could be used for modeling of threshold excitability property of the neurons.

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