Kusmartsev, Vassili F.
Zhang, Wu
Kusmartseva, Anna F.
Balanov, Alexander G.
Janson, Natalia B.
Kusmartsev, Feodor
Ising model – an analysis, from opinions to neuronal states
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.
Dynamical modelling and synchronization phenomena;Mutualistic neural networks;Social network;Social viruses
2017-03-29
https://repository.lboro.ac.uk/articles/Ising_model_an_analysis_from_opinions_to_neuronal_states/9411113