Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients
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| Format: | Preprint |
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2025
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| _version_ | 1866929663478071296 |
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| author | Elia, Cinzia Fabbri, Roberta Núñez, Carmen |
| author_facet | Elia, Cinzia Fabbri, Roberta Núñez, Carmen |
| contents | Nonautonomous bifurcation theory is a growing branch of mathematics, for the insight it provides into radical changes in the global dynamics of realistic models for many real-world phenomena, i.e., into the occurrence of critical transitions. This paper describes several global bifurcation diagrams for nonautonomous first order scalar ordinary differential equations generated by coercive third degree polynomials in the state variable. The conclusions are applied to a population dynamics model subject to an Allee effect that is weak in the absence of migration and becomes strong under a migratory phenomenon whose sense and intensity depend on a threshold in the number of individuals in the population. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_03662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients Elia, Cinzia Fabbri, Roberta Núñez, Carmen Dynamical Systems 37B55, 37G35, 37N25 Nonautonomous bifurcation theory is a growing branch of mathematics, for the insight it provides into radical changes in the global dynamics of realistic models for many real-world phenomena, i.e., into the occurrence of critical transitions. This paper describes several global bifurcation diagrams for nonautonomous first order scalar ordinary differential equations generated by coercive third degree polynomials in the state variable. The conclusions are applied to a population dynamics model subject to an Allee effect that is weak in the absence of migration and becomes strong under a migratory phenomenon whose sense and intensity depend on a threshold in the number of individuals in the population. |
| title | Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients |
| topic | Dynamical Systems 37B55, 37G35, 37N25 |
| url | https://arxiv.org/abs/2501.03662 |