  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 (Differ Equ Dyn Syst 30, 131-159 (2022)) to a wider class of systems
and, in addition, it gives simpler proofs of some already known estimates.
