Predator-prey model with sigmoid functional response
The authors study a classical predator-prey model [\textit{J. L. Jost} et al., J. Theor. Biol. 41, 461--484 (1973)] with sigmoid functional response under the assumption that the denominator in the response function has two distinct real roots. They report on a variety of dynamical phenomena which include global stability of equilibria, the existence of heteroclinic and homoclinic loops, and canard explosion via relaxation oscillation [\textit{M. Krupa} and \textit{P. Szmolyan}, J. Differ. Equations 174(2), 312--368 (2001; Zbl 0994.34032)] or to a homoclinic loop; notably, they argue that the latter is a novel and hitherto unreported phenomenon. Their analysis relies mostly on the geometric singular perturbation theory due to \textit{N. Fenichel} [J. Differ. Equations 31, 53--98 (1979; Zbl 0476.34034)], in particular in their description of heteroclinic connections between the underlying singularities [\textit{X. Chen} and \textit{X. Zhang}, Stud. Appl. Math. 147(1), 300--318 (2021; Zbl 1482.92062)]. Finally, the authors' results are verified and illustrated numerically in the various scenarios considered by them.
scientific article; zbMATH DE number 7867803
scientific article