Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913235393839104 |
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| author | Dueñas, Jesús Longo, Iacopo P. Obaya, Rafael |
| author_facet | Dueñas, Jesús Longo, Iacopo P. Obaya, Rafael |
| contents | This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution are efficient indicators (early-warning signals) of the presence of a tipping point. Precise time-dependent transitions with concave or d-concave variation in the state variable giving rise to scenarios of rate-induced tracking are shown. They are classified depending on the internal dynamics of the set of bounded solutions. Based on this classification, some representative features of these models are investigated by means of a careful numerical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14136 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology Dueñas, Jesús Longo, Iacopo P. Obaya, Rafael Dynamical Systems 37B55, 37G35, 37N25, 34D45 This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution are efficient indicators (early-warning signals) of the presence of a tipping point. Precise time-dependent transitions with concave or d-concave variation in the state variable giving rise to scenarios of rate-induced tracking are shown. They are classified depending on the internal dynamics of the set of bounded solutions. Based on this classification, some representative features of these models are investigated by means of a careful numerical analysis. |
| title | Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology |
| topic | Dynamical Systems 37B55, 37G35, 37N25, 34D45 |
| url | https://arxiv.org/abs/2305.14136 |