Response of traveling waves to transient inputs in neural fields.
Zachary P Kilpatrick and Bard Ermentrout
Phys. Rev. E, 85 (2012) 021910.

Abstract: We analyze the effects of transient stimulation on traveling waves in neural field equations. Neural fields are modeled as integrodifferential equations whose convolution term represents the synaptic connections of a spatially extended neuronal network. The adjoint of the linearized wave equation can be used to identify how a particular input will shift the location of a traveling wave. This wave response function is analogous to the phase response curve of limit cycle oscillators. For traveling fronts in an excitatory network, the sign of the shift depends solely on the sign of the transient input. Equations for the interface and time-dependent speed of the perturbed front also provide complementary estimates of the effective shift. Traveling pulses are analyzed in an asymmetric lateral inhibitory network, and they can be advanced or delayed, depending on the position of spatially localized transient inputs. We also develop bounds on the amplitude of transient input necessary to terminate traveling pulses, based on the global bifurcation structure of the neural field.

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