Dynamical analysis of fractional-order chemostat model

Abstract

The fractional-order differential equations is studied to describe the dynamic behaviour of a chemostat system. The integer-order chemostat model in the form of the ordinary differential equation is extended to the fractional-order differential equations. The stability and bifurcation analyses of the fractional-order chemostat model are investigated using the Adams-type predictor-corrector method. The result shows that increasing or decreasing the value of the fractional order, α , may stabilise the unstable state of a chemostat system and also may destabilised the stable state of the chemostat system depend on the predefined parameter values. The increasing the value of the initial substrate concentration, S 0 may destabilise the stable state of a chemostat system and stabilise the unstable state of the system. Therefore, the running state of a fractional-order chemostat system is affected by the value of α and the value of the initial substrate concentration, S 0. In actual application, the value of the initial substrate should remain at S 0 ≥ 2.54 to ensure that the chemostat system is unstable state. There will be some change in the amount of the cell mass concentration whether increase or decrease when the system is unstable. Therefore, the chemostat system can be well-controlled for the production of cell mass.