Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays
Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays
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DOI：
10.1016/s0167-2789(99)00013-5
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发表时间：
1999-06-15
影响因子：
4
通讯作者：
Coombes, S
中科院分区：
文献类型：
--
作者：
Bressloff, PC;Coombes, S
我们分析行波脉冲耦合积分和消防振荡器与最近邻耦合和延迟相互作用链。这是通过近似的奇异摄动两点（连续）边值问题的锁相方程。后者有一个解决方案，提供了一个自洽的集体振荡频率的值可以找到。我们调查行波的定性行为如何取决于整个链的自然频率的分布和延迟的相互作用的形式。锁相解决方案的线性稳定性分析进行的振荡器的发射时间的扰动方面。示出了当振荡器之间的失谐或耦合强度变得太大时行波如何不稳定。（C）1999 Elsevier Science B.V.保留所有权利。
We analyse travelling waves in a chain of pulse-coupled integrate-and-fire oscillators with nearest-neighbour coupling and delayed interactions. This is achieved by approximating the equations for phase-locking in terms of a singularly perturbed two-point (continuum) boundary value problem. The latter has a solution provided that a self-consistent value for the collective frequency of oscillations can be found. We investigate how the qualitative behaviour of travelling waves depends on the distribution of natural frequencies across the chain and the form of delayed interactions. A linear stability analysis of phase-locked solutions is carried out in terms of perturbations of the firing times of the oscillators. it is shown how travelling waves destabilize when the detuning between oscillators or the strength of the coupling becomes too large. (C)1999 Elsevier Science B.V. All rights reserved.