TY - JOUR
T1 - Trajectory Segmentation and Symbolic Representation of Dynamics of Delayed Recurrent Inhibitory Neural Loops
AU - Ma , Jianfu
AU - Wu , Jianhong
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 129
EP - 150
PY - 2021
DA - 2021/04
SN - 1
DO - http://doi.org/10.12150/jnma.2019.129
UR - https://global-sci.org/intro/article_detail/jnma/18853.html
KW - Multistability, periodic pattern, neural network, time delay, pattern formation, recurrent inhibitory loops.
AB - <p style="text-align: justify;">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.</p>