Quasi-discreted dynamics of a neural net: The lighthouse model

Hermann Haken

Discrete Dynamics in Nature and Society, 2000, vol. 4, 1-14

Abstract:

This paper studies the features of a net of pulse-coupled model neurons, taking into account the dynamics of dendrites and axons. The axonal pulses are modelled by δ -functions. In the case of small damping of dendritic currents, the model can be treated exactly and explicitly. Because of the δ -functions, the phase-equations can be converted into algebraic equations at discrete times. We first exemplify our procedure by two neurons, and then present the results for N neurons. We admit a general dependence of input and coupling strengths on the neuronal indices. In detail, the results are

(1) exact solution of the phase-locked state;

(2) stability of phase-locked state with respect to perturbations, such as phase jumps and random fluctuations, the correlation functions of the phases are calculated;

(3) phase shifts due to spontaneous opening of vesicles or due to failure of opening;

(4) effect of different sensory inputs on axonal pulse frequencies of coupled neurons.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:763864

DOI: 10.1155/S1026022600000182

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