TY - JOUR
T1 - The Dynamics of the Spruce Budworm-Bird System on Time Scale
AU - Zhang , Yao
AU - Pei , Yongzhen
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 764
EP - 781
PY - 2025
DA - 2025/05
SN - 7
DO - http://doi.org/10.12150/jnma.2025.764
UR - https://global-sci.org/intro/article_detail/jnma/24101.html
KW - Slow-fast timescale, relaxation oscillation, canard cycle, predator-prey system.
AB - <p style="text-align: justify;">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.</p>