We study the scenario in which traveling pulses emerge in a prototypical type-I one-dimensional excitable medium, which exhibits two different routes to excitable behavior, mediated by a homoclinic (saddle-loop) and a saddle-node on the invariant cycle bifurcations. We characterize the region in parameter space in which traveling pulses are stable together with the different bifurcations behind either their destruction or loss of stability. In particular, some of the bifurcations delimiting the stability region have been connected, using singular limits, with the two different scenarios that mediated type-I local excitability. Finally, the existence of traveling pulses has been linked to a drift pitchfork instability of localized steady structures.

中文翻译：

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I型可激发介质中行进脉冲的分岔结构

我们研究了行进脉冲出现在原型 I 型一维可激发介质中的情况，该介质表现出两种不同的可兴奋行为途径，由不变循环分岔上的同宿（鞍环）和鞍节点介导。我们描述了参数空间中的区域，其中行进脉冲是稳定的，以及它们破坏或失去稳定性背后的不同分叉。特别是，界定稳定区域的一些分叉已使用奇异限制与介导 I 型局部兴奋性的两种不同情景连接起来。最后，行进脉冲的存在与局部稳定结构的漂移干草叉不稳定性有关。