Year: 2025
Author: Yao Zhang, Yongzhen Pei
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 3 : pp. 764–781
Abstract
We perform a geometric analysis focusing on relaxation oscillations and canard cycles within a singularly perturbed predator-prey system involving budworm and birds. The system undergoes a comprehensive stability analysis, leading to the identification of canard cycles in proximity to the Hopf bifurcation points. The study particularly highlights the transition from smaller Hopf-type cycles to larger relaxation cycles. And the expression of transition threshold $\mu_c(\sqrt{ε})$ of the spruce budworm-bird system is obtained innovatively. Furthermore, numerical simulations are carried out to validate the theoretical findings.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2025.764
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 3 : pp. 764–781
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Slow-fast timescale relaxation oscillation canard cycle predator-prey system.