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

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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)

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.

Suggested Citation

  • Xiuling Li & Siyu Dong, 2025. "Bifurcation Analysis of a Predator–Prey Model with Coefficient-Dependent Dual Time Delays," Mathematics, MDPI, vol. 13(13), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2170-:d:1693531
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    References listed on IDEAS

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    1. Nirapada Santra & Sudeshna Mondal & Guruprasad Samanta, 2022. "Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(20), pages 1-38, October.
    2. Xiuling Li & Siyu Dong & Haotian Fan, 2025. "Bifurcation Analysis of a Class of Food Chain Model with Two Time Delays," Mathematics, MDPI, vol. 13(8), pages 1-26, April.
    3. Das, Bijoy Kumar & Sahoo, Debgopal & Samanta, G.P., 2022. "Impact of fear in a delay-induced predator–prey system with intraspecific competition within predator species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 134-156.
    4. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2024. "Cross-diffusion mediated Spatiotemporal patterns in a predator–prey system with hunting cooperation and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 128-147.
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