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.

本文致力于对生物学中出现的絮凝系统进行数学分析。在一定的充分条件下，我们首先利用Monod型增长函数分别建立了几个分别对应于有界增长率和非单调人均增长率以及无界絮凝率情况的全局存在结果。然后，我们专注于瞬态解的行为，并证明平凡解的稳定性和非平凡正稳态的存在。我们还检查了模型参数所起的作用。我们的论点依赖于不变区域法、不动点理论和谱理论。最后，