Stability of fast travelling pulse solutions of the FitzHugh—Nagumo equations
Stability of fast travelling pulse solutions of the FitzHugh—Nagumo equations
复制标题
FitzHugh-Nagumo 方程快行脉冲解的稳定性
DOI：
10.1007/bf00276548
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发表时间：
1985
影响因子：
1.9
通讯作者：
E. Yanagida
中科院分区：
文献类型：
--
作者：
E. Yanagida
Fitzhugh-Nagumo方程ut=uxx+f(U)-w，ut=b(u-dw)是神经轴突的简化数学描述。如果参数b>；0和d⩾0取得适当，则该方程有两个传播速度不同的行波脉冲解。当b>；0足够小时，我们研究了快脉冲解的稳定性。通过本征值分析，证明了快脉冲解在d>；0时是“指数稳定的”，当d=0时是“边缘稳定的”，但不是指数稳定的。
The FitzHugh-Nagumo equation ut=uxx+f(u)-w, ut=b(u-dw), is a simplified mathematical description of a nerve axon. If the parameters b>0 and d⩾0 are taken suitably, this equation has two travelling pulse solutions with different propagation speeds. We study the stability of the fast pulse solution when b>0 is sufficiently small. It is proved analytically by eigenvalue analysis that the fast pulse solution is “exponentially stable” if d>0, and is “marginally stable” but not exponentially stable if d=0.