Delay induced periodicity in a neural netlet of excitation and inhibition

K. GOPALSAMY, Kui Chiu Issic LEUNG

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Abstract

The dynamical behaviour of a two neuron netlet of excitation and inhibition with a transmission delay is investigated. It is shown that in the absence of delay, the netlet relaxes to the trivial resting state. If the delay is of sufficient magnitude, the network is excited to a temporally periodic cyclic behaviour. The analytical mechanism for the onset of cyclic behaviour is through a Hopf-type bifurcation. Approximate solusions to the periodic output of the netlet is calculated; stability of the temporally periodic cycle is investigated. It is shown that the bifurcation is supercritical. A related discrete version of the continuous time system is formulated. It is found that the discrete system also displays a cyclic behaviour. Results of a number of computer simulations are displayed graphically; the article concludes with a brief neurobiological discussion. Copyright © 1996 Published by Elsevier B.V.
Original languageEnglish
Pages (from-to)395-426
JournalPhysica D: Nonlinear Phenomena
Volume89
Issue number3-4
DOIs
Publication statusPublished - Jan 1996

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Continuous time systems
Periodicity
Neurons
periodic variations
Excitation
Computer simulation
Bifurcation
excitation
Continuous-time Systems
Discrete Systems
Dynamical Behavior
Neuron
Trivial
Computer Simulation
display devices
neurons
Sufficient
Cycle
computerized simulation
Output

Citation

Gopalsamy, K., & Leung, I. (1996). Delay induced periodicity in a neural netlet of excitation and inhibition. Physica D: Nonlinear Phenomena, 89(3-4), 395-426. doi: 10.1016/0167-2789(95)00203-0