J. Nonl. Mod. Anal., 7 (2025), pp. 764-781.
Published online: 2025-05
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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.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.764}, url = {http://global-sci.org/intro/article_detail/jnma/24101.html} }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.