Coexistence solutions of a competition model with two species in a water column

Hua  Nie; Sze-Bi Hsu; Jianhua  Wu

doi:10.3934/dcdsb.2015.20.2691

Article Contents

2015, Volume 20, Issue 8: 2691-2714. Doi: 10.3934/dcdsb.2015.20.2691

This issue Previous Article Balancing survival and extinction in nonautonomous competitive Lotka-Volterra systems with infinite delays Next Article Long time dynamics of a multidimensional nonlinear lattice with memory

Coexistence solutions of a competition model with two species in a water column

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710119
2.
Department of Mathematics, National Tsing Hua University, National Center of Theoretical Science, Hsinchu 300

Received: September 30, 2014

Revised: February 28, 2015

Published: September 2015

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Abstract

Competition between species for resources is a fundamental ecological process, which can be modeled by the mathematical models in the chemostat culture or in the water column. The chemostat-type models for resource competition have been extensively analyzed. However, the study on the competition for resources in the water column has been relatively neglected as a result of some technical difficulties. We consider a resource competition model with two species in the water column. Firstly, the global existence and $L^\infty$ boundedness of solutions to the model are established by inequality estimates. Secondly, the uniqueness of positive steady state solutions and some dynamical behavior of the single population model are attained by degree theory and uniform persistence theory. Finally, the structure of the coexistence solutions of the two-species system is investigated by the global bifurcation theory.

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Mathematics Subject Classification: Primary: 35K57, 35B32; Secondary: 35B50.

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