Coexistence and Extinction in Time-Periodic Volterra-Lotka Type Systems with Nonlocal Dispersal

TL;DR

This paper investigates conditions for coexistence and extinction in time-periodic Volterra-Lotka systems with nonlocal dispersal, extending previous studies to new dynamic environments and revealing key coefficient relations.

Contribution

It establishes the first analysis of coexistence and extinction in time periodic nonlocal dispersal systems, identifying critical coefficient relations for these outcomes.

Findings

Derived conditions for coexistence and extinction.

Linked system coefficients to environmental settings.

Extended understanding to time periodic nonlocal dispersal systems.

Abstract

This paper deals with coexistence and extinction of time periodic Volterra-Lotka type competing systems with nonlocal dispersal. Such issues have already been studied for time independent systems with nonlocal dispersal and time periodic systems with random dispersal, but have not been studied yet for time periodic systems with nonlocal dispersal. In this paper, the relations between the coefficients representing Malthusian growths, self regulations and competitions of the two species have been obtained which ensure coexistence and extinction for the time periodic Volterra-Lotka type system with nonlocal dispersal. The underlying environment of the Volterra-Lotka type system under consideration has either hostile surroundings, or non-flux boundary, or is spatially periodic.