Mechanisms for frequency control in neuronal competition models
Mechanisms for frequency control in neuronal competition models
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DOI：
10.1137/070705842
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发表时间：
2008-01-01
影响因子：
2.1
通讯作者：
Rinzel, John
中科院分区：
文献类型：
--
作者：
Curtu, Rodica;Shpiro, Asya;Rinzel, John
我们分析了A。基于脉冲频率自适应的慢负反馈和相互抑制的两种群网络振铃率模型。两个神经元群体都接受外部恒定输入，其强度决定了系统的动态状态--相同活动水平的稳定状态或周期性振荡或赢家通吃的双稳态。我们证明了振荡出现在系统通过超临界Hopf分岔，他们是反相的。振荡的周期依赖于输入强度在一个非单调的方式，我们表明，增加分支的周期与输入曲线对应的释放机制和减少分支的逃逸机制。在无限慢反馈的极限情况下，我们描述了释放，逃逸和赢家通吃行为发生的条件。对模型的一些扩展也进行了讨论。
We investigate analytically a. ring rate model for a two-population network based on mutual inhibition and slow negative feedback in the form of spike frequency adaptation. Both neuronal populations receive external constant input whose strength determines the system's dynamical state-a steady state of identical activity levels or periodic oscillations or a winner-take-all state of bistability. We prove that oscillations appear in the system through supercritical Hopf bifurcations and that they are antiphase. The period of oscillations depends on the input strength in a nonmonotonic fashion, and we show that the increasing branch of the period versus input curve corresponds to a release mechanism and the decreasing branch to an escape mechanism. In the limiting case of infinitely slow feedback we characterize the conditions for release, escape, and occurrence of the winner-take-all behavior. Some extensions of the model are also discussed.