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Dynamic complexity of a delayed spatiotemporal predator-prey model

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Titel: Dynamic complexity of a delayed spatiotemporal predator-prey model
Autoren: Mohamed Hafdane, Nossaiba Baba, Youssef El Foutayeni, Naceur Achtaich
Quelle: Frontiers in Applied Mathematics and Statistics, Vol 11 (2025)
Verlagsinformationen: Frontiers Media SA, 2025.
Publikationsjahr: 2025
Schlagwörter: T57-57.97, Applied mathematics. Quantitative methods, delay, Turing instability, diffusion, Hopf bifurcation, stability analysis, prey-predator, Probabilities. Mathematical statistics, QA273-280
Beschreibung: 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.
Publikationsart: Article
ISSN: 2297-4687
DOI: 10.3389/fams.2025.1523276
Zugangs-URL: https://doaj.org/article/189c1f40eaef40669ac49420d0cd4f35
Rights: CC BY
Dokumentencode: edsair.doi.dedup.....015e42fe03c3a88b3e3b6f2b15b6d261
Datenbank: OpenAIRE
Beschreibung
Abstract: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.
ISSN:22974687
DOI:10.3389/fams.2025.1523276