Abstract
We introduce a continuum model of neural tissue that includes the effects of spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon nonlocal network connectivity, synaptic response, and the firing rate of a single neuron. We consider a phenomenological model of SFA via a simple state-dependent threshold firing rate function. As without SFA, Mexican-hat connectivity allows for the existence of spatially localized states (bumps). Importantly recent Evans function techniques are used to show that bumps may destabilize leading to the emergence of breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. Simulations confirm our theoretical predictions and illustrate the rich behavior of this model.
Highlights
In this Letter we introduce a continuum model of neural tissue that include the effects of so-called spike frequency adaptation (SFA)
In this Letter we focus on the effects of one such process, namely spike frequency adaptation (SFA)
The generation of an action potential leads to a small calcium influx that increments IAHP, with the end result being a decrease in the firing rate response to persistent stimuli
Summary
In this Letter we introduce a continuum model of neural tissue that include the effects of so-called spike frequency adaptation (SFA). To illustrate this we focus on a one-dimensional neural field model with short-range excitation and long range inhibition, and consider a simple model of SFA. A linear threshold dynamics has previously been considered in [10], and can be traced all the way back to work by Hill in 1936 [14].
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