Global structure of competing model with flocculation in a reaction–diffusion chemostat

Abstract

In this paper, we study a system of reaction–diffusion equations arising from the competition of two competing species for a single limited nutrient with flocculation in an unstirred chemostat. By the conservation principle, we reduce the dimension of the system by eliminating the equation for the nutrient. Then the global structure of the reduced system is studied by the bifurcation theory in its feasible domain. Finally, we use numerical simulation to verify and supplement our theoretical results.

Keywords:

• Chemostat
• flocculation
• reaction–diffusion
• bifurcation
• numerical simulation

Mathematics Subject Classifications:

• 35A01
• 35B32

Acknowledgments

The authors would like to give their sincere thanks to the anonymous referees for their kind and valuable suggestions leading to an improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is supported by the National Natural Science Foundation of China (12201067, 12101075, 12061081) and the Natural Science Basic Research Plan in Shaanxi Province of China (2022JQ-054) and the Fundamental Research Funds for the Central Universities (300102122115).