Successive Canard Explosions in a Singularly Perturbed Spruce-Budworm Model with Holling-II Functional Response
Year: 2024
Author: Liyan Zhong, Jianhe Shen
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 238–264
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.238
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 238–264
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Spruce-Budworm model geometric singular perturbation theory canard explosion inverse canard explosion.