Dynamics of the Non-autonomous Owen-Smith Model

TL;DR

This paper investigates how seasonality influences population dynamics in the Owen-Smith model, establishing conditions for species persistence, extinction, and periodic behavior using advanced mathematical techniques.

Contribution

It provides new necessary and sufficient conditions for permanence and periodic solutions in the non-autonomous Owen-Smith model, incorporating seasonality effects.

Findings

Conditions for herbivore and vegetation permanence

Existence of positive periodic solutions under seasonality

Criteria for herbivore extinction and global stability

Abstract

In this paper we study the dynamics of the general case of Owen-Smith metaphysiological model, to explore the effects of seasonality on population fluctuations. The study will include the permanence, herbivore extinction, global asymptotic stability and existence of positive periodic solutions. Under certain assumptions, we obtained sufficient and necessary conditions which guarantee the permanence of herbivore and vegetation species, and existence of periodic solutions. The techniques we used here are, comparison method of differential equations, Lyapunov method and Brouwer's fixed-point Theorem.