The Analysis of Synaptically Generated Traveling Waves

Mathematical and computational models for the propagation of activity in excitatorily coupled neurons are simulated and analyzed. The basic measurable quantity—velocity—is found for a wide class of models. Numerical bifurcation techniques, asymptotic analysis, and numerical simulations are used to show that there are distinct scaling laws for the velocity as a function of a variety of parameters. In particular, the obvious linear relationships between speed and spatial spread or synaptic decay rate are shown. More surprisingly, it is shown that the velocity scales as a power law with synaptic coupling strength and that the exponent is dependent only on the rising phase of the synapse.

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