We study the analytical integrability of the FitzHugh–Nagumo systems \documentclass[12pt]{minimal}
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\begin{document}$$\dot{x} = z, \dot{y} = b(x - dy), \dot{z} = x(x - 1)(x - a) + y +
cz$$\end{document} in \documentclass[12pt]{minimal}
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\begin{document}$${\mathbb{R}}^3$$\end{document} with parameters \documentclass[12pt]{minimal}
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\begin{document}$$a, b, c, d \in {\mathbb{R}}$$\end{document}