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Neural fields with fast learning dynamic kernel

Abbassian, A. H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s00422-012-0475-9
  3. Abstract:
  4. We introduce a modified-firing-rate model based on Hebbian-type changing synaptic connections. The existence and stability of solutions such as rest state, bumps, and traveling waves are shown for this type of model. Three types of kernels, namely exponential, Mexican hat, and periodic synaptic connections, are considered. In the former two cases, the existence of a rest state solution is proved and the conditions for their stability are found. Bump solutions are shown for two kinds of synaptic kernels, and their stability is investigated by constructing a corresponding Evans function that holds for a specific range of values of the kernel coefficient strength (KCS). Applying a similar method, we consider exponential synaptic connections, where traveling wave solutions are shown to exist. Simulation and numerical analysis are presented for all these cases to illustrate the resulting solutions and their stability
  5. Keywords:
  6. Existence and stability ; Neural field ; Traveling wave ; Bump ; Evans function ; Fast learning ; Model-based OPC ; Neural fields ; State solution ; Synaptic connections ; Traveling wave solution ; Neural networks ; Numerical analysis ; Stability ; Biological model ; Nerve cell network ; Nonlinear system ; Physiology ; Synapse ; Action Potentials ; Computer Simulation ; Humans ; Learning ; Models, Neurological ; Nerve Net ; Neurons ; Nonlinear Dynamics ; Synapses ; Nerve Net
  7. Source: Biological Cybernetics ; Volume 106, Issue 1 , January , 2012 , Pages 15-26 ; 03401200 (ISSN)
  8. URL: http://link.springer.com/article/10.1007%2Fs00422-012-0475-9