A Generalization for Ultradiscrete Limit Cycles in a Certain Type of Max-Plus Dynamical Systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909099460919296 |
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| author | Ohmori, Shousuke Yamazaki, Yoshihiro |
| author_facet | Ohmori, Shousuke Yamazaki, Yoshihiro |
| contents | Dynamical properties of a generalized max-plus model for ultradiscrete limit cycles are investigated.This model includes both the negative feedback model and the Sel'kov model. It exhibits the Neimark-Sacker bifurcation, and possesses stable and unstable ultradiscrete limit cycles. The number of discrete states in the limit cycles can be analytically determined and its approximate relation is proposed. Additionally, relationship between the max-plus model and the two-dimensional normal form of the border collision bifurcation is discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_06230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Generalization for Ultradiscrete Limit Cycles in a Certain Type of Max-Plus Dynamical Systems Ohmori, Shousuke Yamazaki, Yoshihiro Chaotic Dynamics Mathematical Physics Dynamical Systems Dynamical properties of a generalized max-plus model for ultradiscrete limit cycles are investigated.This model includes both the negative feedback model and the Sel'kov model. It exhibits the Neimark-Sacker bifurcation, and possesses stable and unstable ultradiscrete limit cycles. The number of discrete states in the limit cycles can be analytically determined and its approximate relation is proposed. Additionally, relationship between the max-plus model and the two-dimensional normal form of the border collision bifurcation is discussed. |
| title | A Generalization for Ultradiscrete Limit Cycles in a Certain Type of Max-Plus Dynamical Systems |
| topic | Chaotic Dynamics Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2402.06230 |