Bifurcation behavior and a control scheme in a fractional-order chemostat model incorporating delay

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Abstract

In this article, a new fractional-order chemostat model incorporating delay is formulated. Making use of the Lipschitz condition, we confirm the existence and uniqueness of the solution to the formulated model. By defining a reasonable function, we prove that the solution of the proposed model is bounded. The criterion of the stability and Hopf bifurcation emerging from the developed model is established by taking advantage of the stability theory and the Hopf bifurcation theorem of fractional-order differential systems. By contriving two distinctive controllers, we can effectually adjust the stability region and the delay length of the onset of Hopf bifurcation of the developed model. Finally, computer simulation experiments are provided to support the acquired conclusions. The derived results play an important role in balancing the concentrations of the substrate and the cell mass.

Keywords

fractional-order chemostat model / stability / Hopf bifurcation / speed feedback controller / dislocated feedback controller

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