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arXiv · 2311.16735

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

Niklas L. P. Lundström·Gunnar J. Söderbacka
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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 (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.

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Niklas L. P. Lundström, Gunnar J. Söderbacka. 2023-11-28. Estimates of size of cycle in a predator-prey system II. https://arxiv.org/abs/2311.16735

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