TY - JOUR
T1 - Successive Canard Explosions in a Singularly Perturbed Spruce-Budworm Model with Holling-II Functional Response
AU - Zhong , Liyan
AU - Shen , Jianhe
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 238
EP - 264
PY - 2024
DA - 2024/06
SN - 6
DO - http://doi.org/10.12150/jnma.2024.238
UR - https://global-sci.org/intro/article_detail/jnma/23173.html
KW - Spruce-Budworm model, geometric singular perturbation theory,
canard explosion, inverse canard explosion.
AB - <p style="text-align: justify;">By combining geometric singular perturbation theory (GSPT) with
qualitative method, this paper analyzes the phenomenon of successive canard
explosions in a singularly perturbed Spruce-Budworm model with Holling-II
functional response. We select suitable parameters such that the critical curve
is $S$-shaped, and the full model only admits a unique equilibrium. Then, under
the variation of the breaking parameter, it is found that a canard explosion
followed by an inverse canard explosion successively occurs in this model. That
is, a relaxation oscillation arises via the first canard explosion, which persists for a large interval of parameter until it vanishes via the so-called inverse
canard explosion. All these theoretical predictions are verified by numerical
simulations.</p>