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.
Ermentrout
B
B
Department of Mathematics, University of Pittsburgh, PA 15260, USA.
D000818:Animals; D055592:Biophysical Phenomena; D001703:Biophysics; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009431:Neural Conduction / Q000502:physiology; D009474:Neurons / Q000502:physiology; D013569:Synapses / Q000502:physiology*; D013997:Time Factors