论文标题
theta神经元受到延迟反馈的约束：一种自我维持脉冲的典型模型
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing
论文作者
论文摘要
我们考虑一个单一的theta神经元，其及时以Dirac Delta功能的形式延迟自反馈。因为可以明确地解决theta神经元的动力学 - 它是可兴奋的或显示自动的 - 我们能够得出在反馈存在下出现的周期性解决方案的存在和稳定性的代数表达式。这些周期性解决方案的特征是每个延迟间隔一个或多个均匀间隔的脉冲，并且随着延迟时间的增加，多稳定性的量增加。我们介绍了在参数空间中可以找到这些自我维持的振荡的完整描述；特别是，我们为其鞍节分叉的基因座提供了明确的表达式。我们得出的结论是，具有延迟自反馈的theta神经元作为一种典型模型出现：它为理解在其他可激发系统中观察到的脉动动力学提供了一个分析基础，这些动力学会受到延迟的自我耦合。
We consider a single theta neuron with delayed self-feedback in the form of a Dirac delta function in time. Because the dynamics of a theta neuron on its own can be solved explicitly -- it is either excitable or shows self-pulsations -- we are able to derive algebraic expressions for existence and stability of the periodic solutions that arise in the presence of feedback. These periodic solutions are characterized by one or more equally spaced pulses per delay interval, and there is an increasing amount of multistability with increasing delay time. We present a complete description of where these self-sustained oscillations can be found in parameter space; in particular, we derive explicit expressions for the loci of their saddle-node bifurcations. We conclude that the theta neuron with delayed self-feedback emerges as a prototypical model: it provides an analytical basis for understanding pulsating dynamics observed in other excitable systems subject to delayed self-coupling.
