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Ising model – an analysis, from opinions to neuronal states

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journal contribution
posted on 29.03.2017, 14:04 by Vassili F. Kusmartsev, Wu Zhang, Anna F. Kusmartseva, Alexander G. Balanov, Natalia B. Janson, Feodor Kusmartsev
Here we have developed a mathematical model of a random neuron network with two types of neurons: inhibitory and excitatory. Every neuron was modelled as a functional cell with three states, parallel to hyperpolarised, neutral and depolarised states in vivo. These either induce a signal or not into their postsynaptic partners. First a system including just one network was simulated numerically using the software developed in Python. Our simulations show that under physiological initial conditions, the neurons in the network all switch off, irrespective of the initial distribution of states. However, with increased inhibitory connections beyond 85%, spontaneous oscillations arise in the system. This raises the question whether there exist pathologies where the increased amount of inhibitory connections leads to uncontrolled neural activity. There has been preliminary evidence elsewhere that this may be the case in autism and down syndrome [1-4]. At the next stage we numerically studied two mutually coupled networks through mean field interactions. We find that via a small range of coupling constants between the networks, pulses of activity in one network are transferred to the other. However, for high enough coupling there appears a very sudden change in behaviour. This leads to both networks oscillating independent of the pulses applied. These uncontrolled oscillations may also be applied to neural pathologies, where unconnected neuronal systems in the brain may interact via their electromagnetic fields. Any mutations or diseases that increase how brain regions interact can induce this pathological activity resonance. Our simulations provided some interesting insight into neuronal behaviour, in particular factors that lead to emergent phenomena in dynamics of neural networks. This can be tied to pathologies, such as autism, Down's syndrome, the synchronisation seen in parkinson's and the desynchronisation seen in epilepsy. The model is very general and also can be applied to describe social network and social pathologies.

History

School

  • Science

Department

  • Physics

Published in

Proceedings of THE INTERNATIONAL CONFERENCE ENEC-2016 26 – 28 May, 2016 Organized by: HYPERION UNIVERSITY and HYPERION RESEARCH & DEVELOPMENT INSTITUTE

Volume

9

Citation

KUSMARTSEV, V.F. ... et al., 2017. Ising model – an analysis, from opinions to neuronal states. IN: ENEC 2016: Proceedings of the International Conference on Econophysics, New Economy and Complexity, pp. 39-45. Hyperion University and the Hyperion Research and Development Institute in Bucharest, Romania, 26 – 28 May, 2016.

Publisher

Hyperion University

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

01/12/2016

Publication date

2017

Notes

This is a conference paper for ENEC 2016.

ISSN

2069-4350

Language

en