Rinzel J
Biophys J. 1975 Oct;15(10):975-88. doi: 10.1016/S0006-3495(75)85878-4.
A simplified FitzHugh-Nagumo nerve conduction equation with known traveling wave solutions is considered. The spatial stability of these solutions is analyzed to determine which solutions should occur in signal transmission along such a nerve model. It is found that the slower of the two pulse solutions is unstable while the faster one is stable, so the faster one should occur. This agrees with conjectures which have been made about the solutions of other nerve conduction equations. Furthermore for certain parameter values the equation has two periodic wave solutions, each representing a train of impulses, at each frequency less than a maximum frequency wmax. The slower one is found to be unstable and the faster one to be stable, while that at wmax is found to be neutrally stable. These spatial stability results complement the previous results of Rinzel and Keller (1973. Biophys. J. 13: 1313) on temporal stability, which are applicable to the solutions of initial value problems.
考虑一个具有已知行波解的简化FitzHugh-Nagumo神经传导方程。分析这些解的空间稳定性，以确定在沿这种神经模型的信号传输中应该出现哪些解。发现两个脉冲解中较慢的那个是不稳定的，而较快的那个是稳定的，所以应该出现较快的那个。这与关于其他神经传导方程解的猜想一致。此外，对于某些参数值，该方程在每个小于最大频率wmax的频率处有两个周期波解，每个解代表一串脉冲。发现较慢的那个是不稳定的，较快的那个是稳定的，而在wmax处的那个是中性稳定的。这些空间稳定性结果补充了Rinzel和Keller（1973年，《生物物理杂志》13：1313）先前关于时间稳定性的结果，这些结果适用于初值问题的解。
