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Patterns, Memory and Periodicity in Two-Neuron DelayedRecurrent Inhibitory Loops

Published online by Cambridge University Press:  10 March 2010

J. Ma  and
J. Wu
J. Ma
Affiliation:
Department of Mathematics, University of Houston, Houston TX 77204-3008, USA
J. Wu*
Affiliation:
Center for Disease Modeling; Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada
*
* Corresponding author. E-mail:wujh@mathstat.yorku.ca
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Abstract

We study the coexistence of multiple periodic solutions for an analogue of theintegrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayedfeedback, which incorporates the firing process and absolute refractory period. Uponreceiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits aspike with a pattern-related delay, in addition to the synaptic delay. We present atheoretical framework to view the inhibitory signal from the inhibitory neuron as aself-feedback of the excitatory neuron with this additional delay. Our analysis shows thatthe inhibitory feedbacks with firing and the absolute refractory period can generate fourbasic types of oscillations, and the complicated interaction among these basicoscillations leads to a large class of periodic patterns and the occurrence ofmultistability in the recurrent inhibitory loop. We also introduce the average time ofconvergence to a periodic pattern to determine which periodic patterns have the potentialto be used for neural information transmission and cognition processing in the nervoussystem.

Keywords

multistabilityperiodic patternneural networktime delaypattern formationrecurrent inhibitory loops
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 2: Mathematics and neuroscience , 2010 , pp. 67 - 99
Copyright
© EDP Sciences, 2010

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