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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Sari, Sela Tri Indah
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Mathematics

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Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism Sari, Sela Tri Indah; Savitri, Dian
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41044

Abstract

Predator–prey models with nonlinear functional responses provide a robust framework for understanding population regulation and oscillatory dynamics. This study analyzes a three-dimensional predator–prey model incorporating Holling type II functional responses, explicit predator stage structure, and cannibalism. The primary objective is to investigate how adult predation, maturation, and cannibalism parameters influence equilibrium stability and the emergence of oscillations through Hopf bifurcation. Analytical results establish the existence and local stability of a positive coexistence equilibrium. For a biologically relevant parameter set, numerical simulations demonstrate that trajectories converge to the coexistence equilibrium (59.9078, 23.9092, 56.0552). This state is locally asymptotically stable, as the real parts of all Jacobian eigenvalues are negative. Numerical continuation methods are employed to detect Hopf bifurcations induced by key parameters. Two Hopf points are identified for the adult predation rate at 0.4211 and 8.7725, while the maturation rate induces bifurcations at 0.2661 and 0.5271. Additionally, the cannibalism parameter triggers a Hopf bifurcation at 0.1835, initiating periodic population oscillations. These results demonstrate that maturation and cannibalism define distinct instability thresholds, jointly governing the transition from stable coexistence to sustained oscillatory dynamics in stage-structured systems
Co-Authors DIAN SAVITRI