Dynamic complexity of a delayed spatiotemporal predator-prey model
This study investigates a delayed spatiotemporal predator-prey model that incorporates key ecological mechanisms, including the Allee effect, fear-induced prey behavior, Holling type II predation with cooperative hunting, toxicity with delayed effects, and both nonlinear (for prey) and linear (for p...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-06-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2025.1523276/full |
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| author | Mohamed Hafdane Nossaiba Baba Youssef El Foutayeni Naceur Achtaich |
| author_facet | Mohamed Hafdane Nossaiba Baba Youssef El Foutayeni Naceur Achtaich |
| author_sort | Mohamed Hafdane |
| collection | DOAJ |
| description | This study investigates a delayed spatiotemporal predator-prey model that incorporates key ecological mechanisms, including the Allee effect, fear-induced prey behavior, Holling type II predation with cooperative hunting, toxicity with delayed effects, and both nonlinear (for prey) and linear (for predators) fishing pressures. Using tools from the theory of partial differential equations, stability analysis, and Hopf bifurcation theory, we derive the conditions under which stable coexistence or instability emerges. Our results reveal that system stability is maintained below a critical delay threshold, beyond which oscillatory dynamics arise. In the spatial domain, diffusion can either stabilize populations or lead to heterogeneous patterns such as Turing structures and predator-prey segregation, particularly when diffusion is low and delays are significant. Numerical simulations support and illustrate the analytical findings, showing a variety of dynamic behaviors consistent with observed ecological patterns. This work highlights how the interplay between ecological processes, time delays, and spatial effects governs predator-prey dynamics and offers insights relevant to ecosystem management. |
| format | Article |
| id | doaj-art-189c1f40eaef40669ac49420d0cd4f35 |
| institution | OA Journals |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-189c1f40eaef40669ac49420d0cd4f352025-08-20T02:09:51ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-06-011110.3389/fams.2025.15232761523276Dynamic complexity of a delayed spatiotemporal predator-prey modelMohamed Hafdane0Nossaiba Baba1Youssef El Foutayeni2Naceur Achtaich3Analysis, Modeling and Simulation Laboratory, Hassan II University, Casablanca, MoroccoAnalysis, Modeling and Simulation Laboratory, Hassan II University, Casablanca, MoroccoCadi Ayyad University, École Nationale des Sciences Appliquées, Marrakech, MoroccoAnalysis, Modeling and Simulation Laboratory, Hassan II University, Casablanca, MoroccoThis study investigates a delayed spatiotemporal predator-prey model that incorporates key ecological mechanisms, including the Allee effect, fear-induced prey behavior, Holling type II predation with cooperative hunting, toxicity with delayed effects, and both nonlinear (for prey) and linear (for predators) fishing pressures. Using tools from the theory of partial differential equations, stability analysis, and Hopf bifurcation theory, we derive the conditions under which stable coexistence or instability emerges. Our results reveal that system stability is maintained below a critical delay threshold, beyond which oscillatory dynamics arise. In the spatial domain, diffusion can either stabilize populations or lead to heterogeneous patterns such as Turing structures and predator-prey segregation, particularly when diffusion is low and delays are significant. Numerical simulations support and illustrate the analytical findings, showing a variety of dynamic behaviors consistent with observed ecological patterns. This work highlights how the interplay between ecological processes, time delays, and spatial effects governs predator-prey dynamics and offers insights relevant to ecosystem management.https://www.frontiersin.org/articles/10.3389/fams.2025.1523276/fulldiffusionprey-predatorstability analysisdelayHopf bifurcationTuring instability |
| spellingShingle | Mohamed Hafdane Nossaiba Baba Youssef El Foutayeni Naceur Achtaich Dynamic complexity of a delayed spatiotemporal predator-prey model Frontiers in Applied Mathematics and Statistics diffusion prey-predator stability analysis delay Hopf bifurcation Turing instability |
| title | Dynamic complexity of a delayed spatiotemporal predator-prey model |
| title_full | Dynamic complexity of a delayed spatiotemporal predator-prey model |
| title_fullStr | Dynamic complexity of a delayed spatiotemporal predator-prey model |
| title_full_unstemmed | Dynamic complexity of a delayed spatiotemporal predator-prey model |
| title_short | Dynamic complexity of a delayed spatiotemporal predator-prey model |
| title_sort | dynamic complexity of a delayed spatiotemporal predator prey model |
| topic | diffusion prey-predator stability analysis delay Hopf bifurcation Turing instability |
| url | https://www.frontiersin.org/articles/10.3389/fams.2025.1523276/full |
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