Steady State Classification of Allee Effect System
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912212948353024 |
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| author | Song, Kuo Tang, Xiaoxian |
| author_facet | Song, Kuo Tang, Xiaoxian |
| contents | In this paper, we consider the steady state classification problem of the Allee effect system for multiple tribes. First, we reduce the high-dimensional model into several two-dimensional and three-dimensional algebraic systems such that we can prove a comprehensive formula of the border polynomial for arbitrary dimension. Then, we propose an efficient algorithm for classifying the generic parameters according to the number of steady states, and we successfully complete the computation for up to the seven-dimensional Allee effect system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Steady State Classification of Allee Effect System Song, Kuo Tang, Xiaoxian Dynamical Systems Mathematical Physics In this paper, we consider the steady state classification problem of the Allee effect system for multiple tribes. First, we reduce the high-dimensional model into several two-dimensional and three-dimensional algebraic systems such that we can prove a comprehensive formula of the border polynomial for arbitrary dimension. Then, we propose an efficient algorithm for classifying the generic parameters according to the number of steady states, and we successfully complete the computation for up to the seven-dimensional Allee effect system. |
| title | Steady State Classification of Allee Effect System |
| topic | Dynamical Systems Mathematical Physics |
| url | https://arxiv.org/abs/2501.19062 |