Exploration and Control of Bifurcation in a Fractional-Order Delayed Glycolytic Oscillator Model

Abstract

Recently, establishing proper dynamical models to describe the relationship among different chemical substances has become a vital theme in chemistry. In this present article, we set up a new fractional-order delayed glycolytic oscillator model. Utilizing the contraction mapping theorem, we explore the existence and uniqueness of the solution to the involved fractional glycolytic oscillator model with delay. By virtue of some suitable analytical skills, we discuss the non-negativeness of the solution to the established fractional glycolytic oscillator system. Taking advantage of a suitable function, we investigate the boundedness of the fractional glycolytic oscillator system. Exploiting the stability and bifurcation theory of fractional dynamical system, we study the stability and the generation of Hopf bifurcation of the fractional glycolytic oscillator system with delay. Making use of delayed feedback controller and PDα controller, we deal with the Hopf bifurcation control of the fractional glycolytic oscillator system owing delay. Computer simulation results are displayed to support the obtained assertions. The acquired results of this article own great theoretical value in dominating the concentrations of different chemical compositions.