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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.17926 |
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| _version_ | 1866908337224810496 |
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| author | Yin, Hong-Ming |
| author_facet | Yin, Hong-Ming |
| contents | In this paper, we investigate a modified Trojan Y chromosome (TYC) strategy aimed at eradicating invasive species from natural habitats. The proposed mathematical model enhances the original TYC framework by ensuring the non-negativity of population densities and preventing potential solution blow-up. The new model is formulated as a strongly coupled reaction-diffusion system with distinct diffusion coefficients for each species. We first establish the global well-posedness of the system. Subsequently, a stability analysis is conducted. In particular, we demonstrate that the population densities converge to zero when the birth rate for each species falls below a critical threshold. Additionally, we prove the existence of a positive steady-state solution even as the artificially introduced YY-female population density tends to zero as $t$ tends to $\infty$. Furthermore, we identify a bifurcation in the system's solutions as the birth rate crosses the critical value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Modified Mathematical Model Arising from a Trojan Y Chromosome Strategy Yin, Hong-Ming Analysis of PDEs In this paper, we investigate a modified Trojan Y chromosome (TYC) strategy aimed at eradicating invasive species from natural habitats. The proposed mathematical model enhances the original TYC framework by ensuring the non-negativity of population densities and preventing potential solution blow-up. The new model is formulated as a strongly coupled reaction-diffusion system with distinct diffusion coefficients for each species. We first establish the global well-posedness of the system. Subsequently, a stability analysis is conducted. In particular, we demonstrate that the population densities converge to zero when the birth rate for each species falls below a critical threshold. Additionally, we prove the existence of a positive steady-state solution even as the artificially introduced YY-female population density tends to zero as $t$ tends to $\infty$. Furthermore, we identify a bifurcation in the system's solutions as the birth rate crosses the critical value. |
| title | On a Modified Mathematical Model Arising from a Trojan Y Chromosome Strategy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.17926 |