Robust Pulse Generators in an Excitable Medium with Jump-Type Heterogeneity
Robust Pulse Generators in an Excitable Medium with Jump-Type Heterogeneity
复制标题
具有跳跃型异质性的可激励介质中的鲁棒脉冲发生器
DOI：
10.1137/13091261x
复制
发表时间：
2014
影响因子：
2.1
通讯作者：
T.Teramoto
中科院分区：
文献类型：
--
作者：
M.Yadome;Y.Nishiura;T.Teramoto
Heterogeneity is one of the most important and ubiquitous types of external perturbations. We study a spontaneous pulse-generating mechanism in an excitable medium with jump-type heterogeneity. Such a pulse generator (PG) has attracted considerable interest due to the computational potential of pulse waves in physiological signal processing. We first investigate the conditions for the onset of robust-type PGs, and then we show the global bifurcation structure of heterogeneity-induced patterns, including the complex ordered sequence of pulse-generating manners. We devise numerical frameworks to trace the long-term behavior of PGs as periodic solutions, and we detect the associated terminal homoclinic orbits that are homoclinic to a special type of heterogeneity-induced ordered pattern with a hyperbolic saddle. These numerical approaches assist us in identifying a candidate for the organizing center, and producing a variety of PGs as a codimension-two gluing bifurcation, in which two homoclinic trajectories associated with pulse emission and breathing motions form a butterfly configuration.
