Relaxation oscillations of a slow–fast predator–prey model with a piecewise smooth functional response

• Published in: Applied mathematics letters Vol. 113; p. 106852
• Main Authors: Li, Shimin, Wang, Cheng, Wu, Kuilin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2021
• Subjects: Entry–exit function; Geometric singular perturbation theory; Predator–prey model; Relaxation oscillation; Slow–fast system; Entry–exit function; Relaxation oscillation; Geometric singular perturbation theory; Predator–prey model; Slow–fast system
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/j.aml.2020.106852

The paper investigates the relaxation oscillations of a classical predator–prey model, based on the natural ecological assumption that the maximum per capita birth rate of the predator is small in comparison with the intrinsic prey growth rate. Predator’s feeding rate is assumed to be modeled by a piecewise smooth Holling type I functional response including a predator interference, which yields a piecewise smooth slow–fast system. Using geometry singular perturbation theory, we prove that the model has exactly two nested relaxation oscillations surrounding the unique stable node. Additional numerical simulations are provided to verify the analytical results.