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Bazhenov M. V., Rabinovich M. I., Rubchinsky L. L. А simple model for a neuron with complex oscillatory activity. Izvestiya VUZ. Applied Nonlinear Dynamics, 1996, vol. 4, iss. 1, pp. 33-39.

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9 : 612

А simple model for a neuron with complex oscillatory activity

Autors: 
Bazhenov Maksim Vladimirovich, Institute of Applied Physics of the Russian Academy of Sciences
Rabinovich Mihail Izrailevich, University of California, San Diego
Rubchinsky Leonid Lvovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

A simple mathematical model of а neuron describing its oscillatory activity is constructed and investigated. This model in the form of a system of three ordinary differential equations describes both regular behaviour of different patterns in the time dependence of electric membrane potential ара their chaotic dynamics. The features of the neural networks consisting of such elements are discussed.

Key words: 
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Acknowledgments: 
The authors wish to express their gratitude to colleagues Peter Rowat and Alan Selverston at the University of California, San Diego, for discussions on experiments on oscillatory electrical activity of neurons. This work was supported by the Russian Foundation for Basic Research (project 94-02-03263a) and the International Science Foundation (grant NOU 000).
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Received: 
14.04.1995
Accepted: 
27.07.1995
Published: 
05.06.1996
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