Relating the sequential dynamics of excitatory neural networks to synaptic cellular automata

We have developed a new approach for the description of sequential dynamics of excitatory neural networks. Our approach is based on the dynamics of synapses possessing the short-term plasticity property. We suggest a model of such synapses in the form of a second-order system of nonlinear ODEs. In t...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2011-12, Vol.21 (4), p.043124-043124-13
Main Authors: Nekorkin, V. I., Dmitrichev, A. S., Kasatkin, D. V., Afraimovich, V. S.
Format: Article
Language:English
Subjects:
Action Potentials - physiology
Animals
Biological Clocks - physiology
Computer Simulation
Humans
Models, Neurological
Nerve Net - physiology
Neurons - physiology
Nonlinear Dynamics
Synaptic Transmission - physiology
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Summary:We have developed a new approach for the description of sequential dynamics of excitatory neural networks. Our approach is based on the dynamics of synapses possessing the short-term plasticity property. We suggest a model of such synapses in the form of a second-order system of nonlinear ODEs. In the framework of the model two types of responses are realized—the fast and the slow ones. Under some relations between their timescales a cellular automaton (CA) on the graph of connections is constructed. Such a CA has only a finite number of attractors and all of them are periodic orbits. The attractors of the CA determine the regimes of sequential dynamics of the original neural network, i.e., itineraries along the network and the times of successive firing of neurons in the form of bunches of spikes. We illustrate our approach on the example of a Morris-Lecar neural network.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.3657384