Existence and stability of coexistence states in a competition unstirred chemostat |
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| Affiliation: | 1. Department of Mathematics, Southeast University, Nanjing 21189, PR China;2. Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany;1. St. Petersburg State University, 1/1 Ulianovskaya Str., Petrodvorets, 198504, Russia;2. University of Tennessee at Chattanooga, Department of Mathematics, Dept 6956, 615 McCallie Ave., Chattanooga, TN 37403-2598, USA |
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| Abstract: | In this paper, we consider the two similar competing species in a competition unstirred chemostat model with diffusion. The two competing species are assumed to be identical except for their maximal growth rates. In particular, we study the existence and stability of the coexistence states, and the semi-trivial equilibria or the unique coexistence state is the global attractor can be established under some suitable conditions. Our mathematical approach is based on Lyapunov–Schmidt reduction, the implicit function theory and spectral theory. |
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| Keywords: | Existence Stability Lyapunov–Schmidt reduction Chemostat |
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