The Dynamics of the Spruce Budworm-Bird System on Time Scale (Journal of Nonlinear Modeling and Analysis, 2025)
We perform a geometric analysis focusing on relaxation oscillations and canard cycles within a singularly perturbed predator-prey systeminvolving budworm and birds. The system undergoes a comprehensive stability analysis, leading to the identification of canard cycles in proximity tothe Hopf bifurcation points. The study particularly highlights the transitionfrom smaller Hopf-type cycles to larger relaxation cycles. And the expressionof transition threshold $μ_c(\sqrt{ε})$ of the spruce budworm-bird system is obtainedinnovatively. Furthermore, numerical simulations are carried out to validatethe theoretical findings.