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Updated: May 24, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
Neural fields with fast learning dynamic kernel
A H Abbassian1, M Fotouhi, M Heidari
1School of Mathematics, Institute for Research in Fundamental Sciences-IPM, P.O. Box 19395-5746, Tehran, Iran. abbnet@mail.ipm.ir
Abstract:
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.
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