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| Successive Canard Explosions in a Singularly Perturbed Spruce-Budworm Model with Holling-II Functional Response |
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| KeyWord:Spruce-Budworm model, geometric singular perturbation theory, canard explosion, inverse canard explosion |
| Author Name | Affiliation | | Liyan Zhong | School of Basic Medical Sciences, Youjiang Medical University for Nationalities, Baise, 533000, China | | Jianhe Shen | College of Mathematics and Statistics, Fujian Normal University, Fuzhou, Fujian 350007, China
FJKLMAA and Center for Applied Mathematics of Fujian Province (FJNU), Fuzhou, Fujian 350007, China |
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| 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. |
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