Bifurcation Analysis of a Predator–Prey Model with Coefficient-Dependent Dual Time Delays

Xiuling Li and Siyu Dong ()
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Xiuling Li: College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China
Siyu Dong: College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China

Mathematics, 2025, vol. 13, issue 13, 1-23

Abstract: In this paper, a class of two-delay predator–prey models with coefficient-dependent delay is studied. It examines the combined effect of fear-induced delay and post-predation biomass conversion delay on the stability of predator–prey systems. By analyzing the distribution of roots of the characteristic equation, the stability conditions for the internal equilibrium and the existence criteria for Hopf bifurcations are derived. Utilizing normal form theory and the central manifold theorem, the direction of Hopf bifurcations and the stability of periodic solutions are calculated. Finally, numerical simulations are conducted to verify the theoretical findings. This research reveals that varying delays can destabilize the predator–prey system, reflecting the dynamic complexity of real-world ecosystems more realistically.

Keywords: two delays; predator–prey model; Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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