Discrete Dynamics in Nature and Society
Volume 4 (2000), Issue 3, Pages 187-200
Quasi-discreted dynamics of a neural net: The lighthouse model
Institute for Theoretical Physics 1, Center of Synergetics, Pfaffenwaldring 57/4, Stuttgart D-70550, Germany
Received 30 March 1999
Copyright © 2000 Hermann Haken. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 -functions. In the case of small damping of dendritic currents, the model can be treated exactly and explicitly. Because of the -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 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.