New stability criteria for periodic planar Lotka–Volterra systems

In this paper we revisit previous results in the literature dealing with the stability of periodic solutions of periodic predator–prey Lotka–Volterra systems. These results provide stability criteria for the periodic orbits based on boundaries for the average of the coexistence states. In the way it was presented, these boundaries are independent of each other and thus provide a very practical sufficient condition for asymptotically stability. In this note we prove that this independent boundaries can be refined into an intertwined boundary, providing a more sharp sufficient condition.