Homoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator. (Q2925958)

The authors study a two-patch extension of the model suggested by \textit{G. W. Harrison} [Bull. Math. Biol. 48, 137--148 (1986; Zbl 0585.92023)]. A new model describes population dynamics with hysteresis response of the prey to variations of the predator. The prey moves between two patches, risky and safe, in response to varying abundance of predator; the hysteretic flow between the patches is described in terms of the derivative of the Preisach operator. The model is known to exhibit nontrivial dynamic properties including multiple stable equilibria. In the paper under review, numerical evidence for the existence of a robust homoclinic orbit is provided, and a mechanism that leads to appearance of a robust homoclinic loop is discussed.