Yanagita Tatsuo, Suetani Hiromichi, Aihara Kazuyuki
Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0020, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Nov;78(5 Pt 2):056208. doi: 10.1103/PhysRevE.78.056208. Epub 2008 Nov 13.
We study the dynamics of a reaction-diffusion system comprising two mutually coupled excitable fibers. We consider a case in which the dynamical properties of the two fibers are nonidentical due to the parameter mismatch between them. By using the spatially one-dimensional FitzHugh-Nagumo equations as a model of a single excitable fiber, synchronized pulses are found to be stable in some parameter regime. Furthermore, there exists a critical coupling strength beyond which the synchronized pulses are stable for any amount of parameter mismatch. We show the bifurcation structures of the synchronized and solitary pulses and identify a codimension-2 cusp singularity as the source of the destabilization of synchronized pulses. When stable solitary pulses in both fibers disappear via a saddle-node bifurcation on increasing the coupling strength, a reentrant wave is formed. The parameter region, where a stable reentrant wave is observed in direct numerical simulation, is consistent with that obtained by bifurcation analysis.
我们研究了一个由两根相互耦合的可兴奋纤维组成的反应扩散系统的动力学。我们考虑一种情况，即由于两根纤维之间的参数不匹配，它们的动力学特性不相同。通过使用空间一维的FitzHugh-Nagumo方程作为单个可兴奋纤维的模型，发现在某些参数区域同步脉冲是稳定的。此外，存在一个临界耦合强度，超过该强度，对于任何参数不匹配量，同步脉冲都是稳定的。我们展示了同步脉冲和孤立脉冲的分岔结构，并确定了一个二维尖点奇点作为同步脉冲失稳的根源。当通过增加耦合强度使两根纤维中的稳定孤立脉冲通过鞍结分岔消失时，会形成一个折返波。在直接数值模拟中观察到稳定折返波的参数区域与通过分岔分析得到的区域一致。
