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

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.