Coexistence and extinction in Time-Periodic Volterra-Lotka type systems with nonlocal dispersal

Tung Nguyen; Nar Rawal

doi:10.3934/dcdsb.2018080

Article Contents

2018, Volume 23, Issue 9: 3799-3816. Doi: 10.3934/dcdsb.2018080

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Coexistence and extinction in Time-Periodic Volterra-Lotka type systems with nonlocal dispersal

Tung Nguyen^1, and
Nar Rawal^2,

1.
Department of Mathematical Sciences, University of Illinois Springfield, Springfield, IL 62703, USA
2.
Department of Mathematics, Hampton University, Hampton, VA 23668, USA

Received: July 31, 2016

Revised: June 30, 2017

Early access: March 2018

Published: September 2018

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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.

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Mathematics Subject Classification: Primary: 45K05, 92D25, 92D40.

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