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This paper is devoted to the mathematical analysis of a flocculation system that arises in biology. Under certain sufficient conditions, we first establish a few global existence results corresponding, respectively, to the cases of bounded rates and non-monotonic per-capita growth rates as well as to that of unbounded flocculation rates by using Monod-type growth functions. We then focus on the behaviour of the time-dependent solutions, and prove the stability of the trivial solution and the existence of a non-trivial, positive steady state. We also examine the role played by the parameters of the model. Our arguments rely on the invariant region method, fixed point theory, and spectral theory. Finally, we provide some numerical simulations for different values of the diffusion coefficients to show that the competition between species does not depend on the diffusion of nutrients. |
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