A simple geometrical condition for the existence of periodic solutions of planar periodic systems. Applications to some biological models

Global stability of a periodic Holling‐Tanner predator‐prey model

“…Their arguments for the stability of the periodic solution take advantage from the presence of k 2 > 0 in the second equation of (6) and do not work for system (3). In Section 3, we establish sufficient average criteria for the permanence of solutions and the existence of positive periodic solutions of (3) determining an invariant region, depending on t, as in Marva et al 9 In Section 4, we present sufficient conditions guaranteeing the global stability of the unique positive periodic solution (u * (t), v * (t)) of (3). As the first step of our technique, we transform model (3) into the differential system (13) in which the periodic solution becomes the origin.…”