Stability Analysis of Fractional-Order Chemostat Model with Time Delay

The fractional-order chemostat model that considered time delay is studied. Fractional-order differential equations have more benefits for the explanation of memory and the hereditary properties of a system. However, fractional-order differential equations tend to lower the dimensionality of a system. The dimensionality can be infinite-dimensional if the time delay is considered in the differential equation. The stability analysis of the fractional-order chemostat model that considered time delay is studied to examine the effect of time delay on the behaviour of the chemostat system. The numerical simulation was conducted to investigate the fractional-order chemostat model with various values of fractional-order corresponding to different values of time delay. The simulation was performed by using the modified Adams-type predictor–corrector method. The result shows that the stable state transformed into an unstable state or a limit cycle at an appropriate time delay value. As the fractional-order value decreased, a higher value of time delay has to be considered. Therefore, the suitable time delay value can be appropriately selected to ensure that the chemostat system’s dynamic behaviour is constantly unstable, which is appropriate for cell mass growth.