We introduce a geometrical extension of the FitzHugh–Nagumo equations describing propagation of electrical impulses in nerve axons. In this extension, the axon is modeled as a warped cylinder, rather than a straight line, as is usually done. Nearly planar pulses propagate on its surface, along the cylindrical axis, as is the case with real axons. We prove the stability of electrical impulses for a straight (or standard) cylinder and existence and stability of pulse-like solutions for warped cylinders whose radii are small and vary slowly along their lengths and depend also on the azimuthal angle.

中文翻译：

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圆柱表面上FitzHugh-Nagumo方程的近脉冲解

我们介绍了描述神经轴突中电脉冲传播的FitzHugh-Nagumo方程的几何扩展。在此扩展中，轴突建模为弯曲的圆柱体，而不是通常的直线。像真正的轴突一样，近乎平面的脉冲沿着圆柱轴在其表面传播。我们证明了直线（或标准）圆柱体的电脉冲的稳定性，以及半径较小且沿其长度缓慢变化且还取决于方位角的弯曲圆柱体的类脉冲解的存在性和稳定性。