Coherent structures near the boundary between excitable and oscillatory media
Coherent structures near the boundary between excitable and oscillatory media
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可兴奋介质和振荡介质之间边界附近的相干结构
DOI：
10.1080/14689360903325071
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
A. Scheel
中科院分区：
文献类型：
--
作者：
J. Bellay;A. Scheel
我们研究了反应扩散系统附近的参数值，这些参数值标志着从可激介质到振荡介质的转变。我们分析了当参数进入振荡区时，作为激励脉冲极限的陡脉冲附近行波的存在性和稳定性。通过分析一个共维二同斜鞍节点/轨道翻转分岔，得到了该极限剖面附近的行波。主要结果表明，这种跃迁恰好有两种一般情况，通过脉冲之间的相互作用系数的符号来区分。在这两种情况下，我们发现稳定的快速锋面，不稳定的慢锋面，稳定的激励脉冲，触发波和相位波。在斥力相互作用下触发波和相波都是稳定的，在吸引相互作用下触发波和相波都是不稳定的。
We investigate reaction–diffusion systems near parameter values that mark the transition from an excitable to an oscillatory medium. We analyse the existence and stability of travelling waves near a steep pulse that arises as the limit of excitation pulses when parameters cross into the oscillatory regime. Travelling waves near this limiting profile are obtained by analysing a codimension-two homoclinic saddle-node/orbit-flip bifurcation. The main result shows that there are precisely two generic scenarios for such a transition, distinguished by the sign of an interaction coefficient between pulses. In both scenarios, we find stable fast fronts, unstable slow fronts, stable excitation pulses, and trigger and phase waves. Both trigger and phase waves are stable for repulsive interaction and both are unstable for attractive interaction.