Competition models with Allee effects |
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| Authors: | G Livadiotis L Assas S Elaydi E Kwessi D Ribble |
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| Institution: | 1. Southwest Research Institute, San Antonio, TX, USAglivadiotis@swri.edu;3. Department of Mathematics, King Abdul-Aziz University, Jeddah, Saudi Arabia;4. Department of Mathematics, Um-Al-Qurah University, Makkah, Saudi Arabia;5. Department of Mathematics, Trinity University, San Antonio, TX, USA;6. Center of Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Tecnico, Technical University of Lisbon, Lisbon, Portugal;7. Department of Biology, Trinity University, San Antonio, TX, USA |
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| Abstract: | In this paper, we study a generalized two-species contest-competition model with an Allee effect. We provide a complete analysis of the global dynamics of the system. In particular, we determine all the invariant manifolds, the extinction, the exclusion and the coexistence regions. We use tools from topology and dynamical systems to show that all orbits must converge to one of the equilibrium points of the system. The analysis shows that there are several potential scenarios including competition coexistence, exclusion and extinction. |
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| Keywords: | Allee effect global dynamics extinction region monotonicity |
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