Stationary wave solutions of a system of reaction-diffusion equations derived from the Fitzhugh-Nagumo equations
Stationary wave solutions of a system of reaction-diffusion equations derived from the Fitzhugh-Nagumo equations
复制标题
由 Fitzhugh-Nagumo 方程导出的反应扩散方程组的驻波解
DOI：
10.1137/0144008
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发表时间：
1984
影响因子：
1.9
通讯作者：
W. Troy
中科院分区：
文献类型：
--
作者：
G. Klaasen;W. Troy
我们考虑FitzHugh-Nagumo模型的扩展，即$\varepsilon > 0,\gamma > 0,D_1 > 0,D_2 > 0$和$f(u)$为三次的系统\[ u_t = D_1 u_{xx} + f(u) - w,\qquad w_t = D_2 w_{xx} + \varepsilon (u - \gamma w) \]。我们允许$\gamma $很大，这意味着有三个常数解。我们证明了在一个适当的参数范围内，系统具有与时间无关的脉冲解和无限个周期解。根据特定参数的选择，我们表明脉冲解导致第一常数解或第三常数解。
We consider an extension of the FitzHugh–Nagumo model, namely the system \[ u_t = D_1 u_{xx} + f(u) - w,\qquad w_t = D_2 w_{xx} + \varepsilon (u - \gamma w) \] where $\varepsilon > 0,\gamma > 0,D_1 > 0,D_2 > 0$ and $f(u)$ is cubic. We allow $\gamma $ to be large which implies that there are three constant solutions. We show that over an appropriate range of parameters the system has time independent pulse solutions and an infinite number of periodic solutions. Depending on the particular choice of parameters, we show that the pulse solution leads to either the first constant solution or the third constant solution.