Dynamics of a class of time-period strongly 2-cooperative system: integer-valued Lyapunov function and embedding property of limit sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911758581497856 |
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| author | Gao, Mengmeng Zhou, Dun |
| author_facet | Gao, Mengmeng Zhou, Dun |
| contents | We construct an integer-valued Lyapunov function $σ(\cdot)$ for generalized negative cyclic feedback system; and prove that $σ(\cdot)$ on any $ω$-limit set which generated by Poincaré mapping of bounded solution of such strongly $2$-cooperative system is constant. Therefore, the $ω$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of a class of time-period strongly 2-cooperative system: integer-valued Lyapunov function and embedding property of limit sets Gao, Mengmeng Zhou, Dun Dynamical Systems Classical Analysis and ODEs We construct an integer-valued Lyapunov function $σ(\cdot)$ for generalized negative cyclic feedback system; and prove that $σ(\cdot)$ on any $ω$-limit set which generated by Poincaré mapping of bounded solution of such strongly $2$-cooperative system is constant. Therefore, the $ω$-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. |
| title | Dynamics of a class of time-period strongly 2-cooperative system: integer-valued Lyapunov function and embedding property of limit sets |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.08137 |