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| Trajectory Segmentation and SymbolicRepresentation of Dynamics of Delayed RecurrentInhibitory Neural Loops |
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| KeyWord:Multistability periodic pattern neural network time delay pat-
tern formation recurrent inhibitory loops |
| Author Name | Affiliation | | Jianfu Ma | Laboratory for Industrial and Applied Mathematics, Department of Mathe-
matics and Statistics, Fields-CQUM Laboratory of Mathematics for Public
Health, York University, Toronto, Ontario, M3J 1P3, Canada | | Jianhong Wu | Laboratory for Industrial and Applied Mathematics, Department of Mathe-
matics and Statistics, Fields-CQUM Laboratory of Mathematics for Public
Health, York University, Toronto, Ontario, M3J 1P3, Canada |
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| 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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