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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Main Authors: Mohamed Hafdane, Nossaiba Baba, Youssef El Foutayeni, Naceur Achtaich
Format: Article
Language:English
Published: Frontiers Media S.A. 2025-06-01
Series:Frontiers in Applied Mathematics and Statistics
Subjects:
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.
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issn 2297-4687
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publisher Frontiers Media S.A.
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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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AT naceurachtaich dynamiccomplexityofadelayedspatiotemporalpredatorpreymodel