| Volume 9, Number 3, 2019, Pages 981-1006 DOI：10.11948/2156-907X.20180195 |
| A microbial continuous culture system with diffusion and diversified growth |
| Jingli Ren,Ying Xu |
| Keywords:Continuous culture, diffusion, diversified growth, stability, steady state bifurcation. |
| Abstract: |
| A reaction-diffusion model is presented to describe the microbial continuous culture with diversified growth. The existence of nonnegative solutions and attractors for the system is obtained, the stability of steady states and the steady state bifurcation are studied under three growth conditions. In the case of no growth inhibition or only product inhibition, the system admits one positive constant steady state which is stable; in the case of growth inhibition only by substrate, the system can have two positive constant steady states, explicit conditions of the stability and the steady state bifurcation are also determined. In addition, numerical simulations are given to exhibit the theoretical results. |
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