Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type

TL;DR

This paper proves the existence of positive periodic solutions in predator-prey models of Leslie-Gower or Holling-Tanner type with periodic coefficients, using operator methods without restrictive conditions.

Contribution

It introduces a novel operator method approach to establish positive periodic solutions in these predator-prey systems under minimal assumptions.

Findings

Existence of positive periodic solutions proven

Method applicable to delayed systems with minor modifications

No restrictive conditions on coefficients besides positivity and periodicity

Abstract

In this paper, we consider periodic predator-prey systems of Leslie-Gower or Holling-Tanner type, assuming that the coefficients are continuous positive $\omega$-periodic functions. We prove an existence of positive $\omega$-periodic solutions by means of operator method in Banach spaces with cones. No constructive conditions are required for the coefficients, besides the positivity and periodicity. At the end we point out that the used approach can be applied with minor changes for proving the existence of positive $\omega$-periodic solutions even in the case of certain delays.