Positive solutions of a diffusive two competitive species model with saturation

Aung Zaw Myint

doi:10.3934/dcdsb.2021199

Article Contents

2022, Volume 27, Issue 7: 3625-3641. Doi: 10.3934/dcdsb.2021199

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Positive solutions of a diffusive two competitive species model with saturation

Aung Zaw Myint^,

Department of Mathematics, University of Mandalay, Mandalay 05032, Myanmar

^* Corresponding author: Aung Zaw Myint
^* Corresponding author: Aung Zaw Myint

Received: April 2021

Early access: August 9, 2021

Published online: August 9, 2021

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Abstract

In this paper, the positive solutions of a diffusive two competitive species model with Bazykin functional response are investigated. We give the a priori estimates and compute the fixed point indices of trivial and semi-trivial solutions. And obtain the existence of solution and demonstrate the bifurcation of a coexistence state emanating from semi-trivial solutions. Finally, multiplicity and stability results are presented.

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Mathematics Subject Classification: Primary: 35J57, 35B09, 35B32, 35B35; Secondary: 92B05.

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Figure 1. The existence of coexistence states and bifurcation lines

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Figure 2. For $ \alpha\gg 1 $, the existence and multiplicity of coexistence states

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Figure 3. For $ \beta\gg 1 $, the existence and multiplicity of coexistence states

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