Bezekci B, Biktashev V N
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom.
Chaos. 2017 Sep;27(9):093916. doi: 10.1063/1.4999472.
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.
我们研究了FitzHugh-Nagumo模型中激发波的起始问题。我们的方法遵循早期的研究工作，其基于这样一种思想：将传播波吸引子盆地与静止状态吸引子盆地之间的边界近似为一个临界解的稳定流形。在此，我们通过使用两个小参数进行奇异摄动，得到了该理论基本要素的解析表达式，这两个小参数分别是激活剂和抑制剂的时间尺度分离以及激活剂动力学中的阈值。这就得到了强度-持续时间曲线的一个封闭解析表达式。
