# Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 2, page 67-99
- ISSN: 0973-5348

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topMa, J., and Wu, J.. "Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops." Mathematical Modelling of Natural Phenomena 5.2 (2010): 67-99. <http://eudml.org/doc/197647>.

@article{Ma2010,

abstract = {We study the coexistence of multiple periodic solutions for an analogue of the
integrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayed
feedback, which incorporates the firing process and absolute refractory period. Upon
receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a
spike with a pattern-related delay, in addition to the synaptic delay. We present a
theoretical framework to view the inhibitory signal from the inhibitory neuron as a
self-feedback of the excitatory neuron with this additional delay. Our analysis shows that
the inhibitory feedbacks with firing and the absolute refractory period can generate four
basic types of oscillations, and the complicated interaction among these basic
oscillations leads to a large class of periodic patterns and the occurrence of
multistability in the recurrent inhibitory loop. We also introduce the average time of
convergence to a periodic pattern to determine which periodic patterns have the potential
to be used for neural information transmission and cognition processing in the nervous
system. },

author = {Ma, J., Wu, J.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {multistability; periodic pattern; neural network; time delay; pattern formation; recurrent inhibitory loops; integrate-and-fire neuron model},

language = {eng},

month = {3},

number = {2},

pages = {67-99},

publisher = {EDP Sciences},

title = {Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops},

url = {http://eudml.org/doc/197647},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Ma, J.

AU - Wu, J.

TI - Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/3//

PB - EDP Sciences

VL - 5

IS - 2

SP - 67

EP - 99

AB - We study the coexistence of multiple periodic solutions for an analogue of the
integrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayed
feedback, which incorporates the firing process and absolute refractory period. Upon
receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a
spike with a pattern-related delay, in addition to the synaptic delay. We present a
theoretical framework to view the inhibitory signal from the inhibitory neuron as a
self-feedback of the excitatory neuron with this additional delay. Our analysis shows that
the inhibitory feedbacks with firing and the absolute refractory period can generate four
basic types of oscillations, and the complicated interaction among these basic
oscillations leads to a large class of periodic patterns and the occurrence of
multistability in the recurrent inhibitory loop. We also introduce the average time of
convergence to a periodic pattern to determine which periodic patterns have the potential
to be used for neural information transmission and cognition processing in the nervous
system.

LA - eng

KW - multistability; periodic pattern; neural network; time delay; pattern formation; recurrent inhibitory loops; integrate-and-fire neuron model

UR - http://eudml.org/doc/197647

ER -

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