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Global Dynamical Behavior of FitzHugh–Nagumo Systems with Invariant Algebraic Surfaces

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Abstract

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.

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Acknowledgements

The second author is partially supported by NNSF of China(11771282, 11931016), Science and Technology Innovation Action Program of STCSM(20JC1413200). The third author is partially supported by NNSF of China(11871334, 12071284).

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  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Liwei Zhang, Jiang Yu & Xiang Zhang

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  1. Liwei Zhang
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  2. Jiang Yu
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  3. Xiang Zhang
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Correspondence to Jiang Yu.

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Zhang, L., Yu, J. & Zhang, X. Global Dynamical Behavior of FitzHugh–Nagumo Systems with Invariant Algebraic Surfaces. Qual. Theory Dyn. Syst. 20, 16 (2021). https://doi.org/10.1007/s12346-021-00452-2

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