在這篇論文中，我們感興趣的是Fitzhugh-Nagumo方程系統的週期解。首先使用變分法
證明解的存在性。同時我們也透過數值方法來觀察這些週期解的多樣性。藉由差分與
梯度下降法，這套疊代演算法可以協助我們進一步了解週期解的形態。

In this thesis, we study the pattern formation in the FitzHugh-Nagumo equations. This
is an activator-inhibitor type reaction-diffusion system and there is a variational structure
which will be used in our investigation. We show the existence of periodic solutions by using variational argument to find a minimizer. We also work on the numerical computation
on such solutions.

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