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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 NameAffiliation
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.