Abstract
By using geometric singular perturbation theory and a new entry–exit function, this paper is concerned with the number and stability of relaxation oscillations in a slow–fast predator–prey model with weak Allee effect and Holling-IV functional response. We find that this model can admit at most three nested (large amplitude) relaxation oscillations. Two of them are stable while the other one is unstable. Also we find that the relative heights between the folded points and the transcritical bifurcation point of the critical curves affect the number and stability of relaxation oscillations greatly. Compared with the existing models, the weak Allee effect makes the model possess one more sustained oscillations, i.e., the weak Allee effect promotes the stability of the predator–prey system. The theoretical predictions about the number and stability of relaxation oscillations are verified by numerical simulations.
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