@Article{JNMA-6-2,
author = {Zhong, Liyan and Shen, Jianhe},
title = {Successive Canard Explosions in a Singularly Perturbed Spruce-Budworm Model with Holling-II Functional Response},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2024},
volume = {6},
number = {2},
pages = {238--264},
abstract = {<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>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2024.238},
url = {https://global-sci.com/article/91151/successive-canard-explosions-in-a-singularly-perturbed-spruce-budworm-model-with-holling-ii-functional-response}
}