Estimates of size of cycle in a predator-prey system II

Abstract

We prove estimates for the maximal and minimal predator and prey populations on the unique limit cycle in a standard predator-prey system.Our estimates are valid when the cycle exhibits small predator and prey abundances and large amplitudes.The proofs consist of constructions of several Lyapunov-type functions and derivation of a large number of non-trivial estimates,and should be of independent interest.This study generalizes results proved by the authors in [11] to a wider class of systems and, in addition, it gives simpler proofs of some already known estimates.