Bumps, breathers, and waves in a neural network with spike frequency adaptation

被引:81
作者
Coombes, S [1 ]
Owen, MR [1 ]
机构
[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England
基金
英国工程与自然科学研究理事会;
关键词
D O I
10.1103/PhysRevLett.94.148102
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
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页数:4
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