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arXiv · 2401.08137

Dynamics of a class of time-period strongly 2-cooperative system: integer-valued Lyapunov function and embedding property of limit sets

Mengmeng Gao·Dun Zhou
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Abstract

We construct an integer-valued Lyapunov function $\sigma(\cdot)$ for generalized negative cyclic feedback system; and prove that $\sigma(\cdot)$ on any $\omega$-limit set which generated by Poincar\'{e} mapping of bounded solution of such strongly $2$-cooperative system is constant. Therefore, the $\omega$-limit can be continuously embedded into a compact subset of a two-dimensional plane. Finally, a dissipative condition is given to ensure that all orbits of such system are bounded.

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Mengmeng Gao, Dun Zhou. 2024-01-16. Dynamics of a class of time-period strongly 2-cooperative system: integer-valued Lyapunov function and embedding property of limit sets. https://arxiv.org/abs/2401.08137

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