Stability and bifurcation control for a fractional-order chemostat model with time delays and incommensurate orders

Xiaomeng Ma; Zhanbing Bai; Sujing Sun; Xiaomeng Ma; Zhanbing Bai; Sujing Sun

doi:10.3934/mbe.2023020

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 437-455. doi: 10.3934/mbe.2023020

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Stability and bifurcation control for a fractional-order chemostat model with time delays and incommensurate orders

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 01 August 2022 Revised: 09 September 2022 Accepted: 25 September 2022 Published: 10 October 2022

In this paper, a delayed fractional Lotka-Volterra food chain chemostat model with incommensurate orders is proposed, and the effect on system stability and bifurcation of this model are discussed. First, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Taking the time delay as the bifurcation parameter, the relevant characteristic equations are analyzed, and the conditions for Hopf bifurcation are proposed. The results show that the controller can fundamentally affect the stability of the system, and that they both have an important impact on the generation of bifurcation at the same time. Finally, numerical simulation is carried out to support the theoretical data.
- fractional system,
- time delay,
- stability,
- control,
- chemostat model,
- Hopf bifurcation,
- incommensurate orders
Citation: Xiaomeng Ma, Zhanbing Bai, Sujing Sun. Stability and bifurcation control for a fractional-order chemostat model with time delays and incommensurate orders[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 437-455. doi: 10.3934/mbe.2023020

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Abstract

In this paper, a delayed fractional Lotka-Volterra food chain chemostat model with incommensurate orders is proposed, and the effect on system stability and bifurcation of this model are discussed. First, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Taking the time delay as the bifurcation parameter, the relevant characteristic equations are analyzed, and the conditions for Hopf bifurcation are proposed. The results show that the controller can fundamentally affect the stability of the system, and that they both have an important impact on the generation of bifurcation at the same time. Finally, numerical simulation is carried out to support the theoretical data.

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