We propose a mathematical model for a class of predator–prey systems more complex than the usual one, involving a commensalism effect consisting in an influence of the predator on the sustainability of the prey. This effect induces interesting new features, including bi-stability (two attractors with disjoint attraction basins). The question of the possibility of reaching a certain attractor starting from initial conditions with a small population of predators, which presents an interest from the vewpoint of the onset of the predator in evolution, is addressed. We propose two possibilities: the classical one involving adapted conditions in the far past and a new (up to our knowledge) one using biodiversity, specifically the presence of another predator which operates as a starter, being displaced in the sequel.
Acta Biotheoretica – Springer Journals
Published: Dec 1, 2021
Keywords: Predator–prey systems; Bi-stability; Excitability; “Diversity–stability debate”; Primary 92D25 Population dynamics; 92D40 Ecology; 37G15 Bifurcations of limit cycles and periodic orbits