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

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.

Keywords

• fractional system
• time delay
• stability
• control
• chemostat model
• hopf bifurcation
• incommensurate orders