Delay-induced bubbling in a harvested plankton-fish model: A study on the role of two fish predators

Article Type

Research Article

Publication Title

Nonlinear Dynamics

Abstract

A mathematical model is developed to address the dynamic complexities of plankton-fish systems, focusing on harvesting pressures and gestation delays. The model accounts for distinct predation strategies, with the first fish predator following a type-I functional response and the second exhibiting a type-IV response. We examine the local stability of equilibria and explore the potential for Hopf bifurcation in delayed systems. Utilizing the center manifold theorem and normal form theory, we derive explicit formulas that help identify the direction of Hopf bifurcation and assess the stability of the resulting periodic solutions. To support our theoretical results, we conduct numerical simulations that confirm the findings. Our results indicate that a moderate amount of harvesting of first fish predators benefits the system. The gestation delay plays a crucial role by notifying prior bifurcation occurrence and delay-induced bubbling phenomena. This study offers insights into the dynamic interplay of harvesting, gestation delay, and predator competition. The model’s findings contribute to fisheries management and conservation, emphasizing strategies to optimize sustainable practices while preserving ecological integrity in multi-predator systems.

First Page

22143

Last Page

22165

DOI

10.1007/s11071-025-11285-y

Publication Date

8-1-2025

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