Mathematical analysis of the direction and stability of Hopf-bifurcation in a prey-predator model including a maturation and hunting delay
Year: 2025
Type: article
Abstract: In this study, we present and analyze a delayed prey-predator model to simultaneously describe the effects of predator maturation and hunting delay. The interaction between prey and predator species is followed by Monod-Haldane-type functional response. First, we show that the model without delay is mathematically and biologically well-posed through the study of the existence, uniqueness, and boundedness of the solution. Moreover, we evaluate the criteria for local and global asymptotic stability of the unique coexistence equilibrium point by using respectively the Routh-Hurwitz criterion and the Lyapunov principle. Then, concerning the delayed model we show that the system undergoes a Hopf-bifurcation from a threshold value of the delay. Furthermore, we apply the theory of normal form method and center manifold theorem to study the direction and stability of Hopf-bifurcation in order to simultaneously highlight the effects of the predator's delayed maturation and hunting in both species. Finally, numerical investigations have been carried out to support our theoretical results.
Source: Research in Mathematics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: Erasmus+
OpenAlex ID: W7117366136