Wavy fronts in a hyperbolic FitzHugh-Nagumo system and the effects of cross diffusion.
Wavy fronts in a hyperbolic FitzHugh-Nagumo system and the effects of cross diffusion.
复制标题
双曲 FitzHugh-Nagumo 系统中的波阵面和交叉扩散的影响。
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
W. Horsthemke
中科院分区：
文献类型：
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作者：
E. Zemskov;M. Tsyganov;W. Horsthemke
我们研究了FitzHugh-Nagumo（也称为Bonhoeffer-van der Pol）反应扩散系统的双曲版本。为了能够得到解析结果，我们采用了非线性动力学项的分段线性近似。将双曲型系统与标准抛物型FitzHugh-Nagumo系统进行了比较。我们完整地描述了波前的动力学，并讨论了速度方程的性质。在双曲系统和抛物系统中，行进锋的非平衡伊辛-布洛赫分岔也会发生。在双曲线情况下，波的绝对传播速度通常比抛物线情况下的波低。我们发现了具有对角扩散矩阵的FitzHugh-Nagumo模型的双曲和抛物线锋面轨迹在相平面上重合的有趣特征，这是自扩散的情况，而对于具有交叉扩散的系统则不同。
We study a hyperbolic version of the FitzHugh-Nagumo (also known as the Bonhoeffer-van der Pol) reaction-diffusion system. To be able to obtain analytical results, we employ a piecewise linear approximation of the nonlinear kinetic term. The hyperbolic version is compared with the standard parabolic FitzHugh-Nagumo system. We completely describe the dynamics of wavefronts and discuss the properties of the speed equation. The nonequilibrium Ising-Bloch bifurcation of traveling fronts is found to occur in the hyperbolic case as well as in the parabolic system. Waves in the hyperbolic case typically propagate with lower speeds, in absolute value, than waves in the parabolic one. We find the interesting feature that the hyperbolic and parabolic front trajectories coincide in the phase plane for the FitzHugh-Nagumo model with a diagonal diffusion matrix, which is the case of self-diffusion, and differ for the system with cross diffusion.