Successive Canard Explosions in a Singularly Perturbed Spruce-Budworm Model with Holling-II Functional Response (Journal of Nonlinear Modeling and Analysis, 2024)
By combining geometric singular perturbation theory (GSPT) withqualitative method, this paper analyzes the phenomenon of successive canardexplosions in a singularly perturbed Spruce-Budworm model with Holling-IIfunctional response. We select suitable parameters such that the critical curveis $S$-shaped, and the full model only admits a unique equilibrium. Then, underthe variation of the breaking parameter, it is found that a canard explosionfollowed by an inverse canard explosion successively occurs in this model. Thatis, a relaxation oscillation arises via the first canard explosion, which persists for a large interval of parameter until it vanishes via the so-called inversecanard explosion. All these theoretical predictions are verified by numericalsimulations.
Keywords: Spruce-Budworm model; geometric singular perturbation theory; canard explosion; inverse canard explosion.