In this paper, we characterize the global dynamical behaviors of FitzHugh–Nagumo system \(\dot{x}=z\), \(\dot{y}=b(x-dy)\), \(\dot{z}=x(x-1)(x-a)+y+cz\) which has invariant algebraic surfaces. As byproducts, we obtain some new dynamical phenomena related to the invariant surfaces at the infinity, which does not appear previously in the study of other models. In addition, since the system restricted to the invariant algebraic surfaces is not analytic, we adopt some new techniques to overcome this difficulty.

中文翻译：

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具有不变代数曲面的FitzHugh-Nagumo系统的整体动力学行为

在本文中，我们表征了FitzHugh–Nagumo系统\（\ dot {x} = z \），\（\ dot {y} = b（x-dy）\），\（\ dot {z } = x（x-1）（xa）+ y + cz \）具有不变的代数曲面。作为副产品，我们获得了一些与无穷大处的不变曲面有关的新动力学现象，这在以前的其他模型研究中并未出现。另外，由于限于不变代数曲面的系统无法解析，因此我们采用了一些新技术来克服这一困难。