Phase plane analysis of a neuron map-based model by determining periodicities

Ramírez Ávila, G. M;


We study the Rulkov model phase plane, a two-dimensional map-based model that describes the behavior of a neuron. Keeping constant one of the three parameters, we obtain phase planes showing well-defined periodicities. We show the importance of the parameter \i identifying the periodicities and the number of spikes per burst, quantities that are related between them by a linear relationship. The zones in which these periodicities are well-defined exhibit in some cases, shapes similar to those appearing in some palm-tree patterns observed both in trunks and in leaves. The detailed determination and description of these periodicity zones could be the basis for a further study on synchronization of nonidentical neurons in regions in which the domain of the parameter values ensure the fact to work with the same periodicity. We also analyze the reliability and the limitations of this method

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