Trajectory Segmentation and Symbolic Representation of Dynamics of Delayed Recurrent Inhibitory Neural Loops
Year: 2019
Author: Jianfu Ma, Jianhong Wu
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 2 : pp. 129–150
Abstract
We develop a general symbolic dynamics framework to examine the dynamics of an analogue of the integrate-and-fire neuron model of recurrent inhibitory loops with delayed feedback, which incorporates the firing procedure and absolute refractoriness. We first show that the interaction of the delay, the inhibitory feedback and the absolute refractoriness can generate three basic types of oscillations, and these oscillations can be pinned together to form interesting coexisting periodic patterns in the case of short feedback duration. We then develop a natural symbolic dynamics formulation for the segmentation of a typical trajectory in terms of the basic oscillatory patterns, and use this to derive general principles that determine whether a periodic pattern can and should occur.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.129
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 2 : pp. 129–150
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Multistability periodic pattern neural network time delay pattern formation recurrent inhibitory loops.