Abstract
Building differential dynamical systems to describe the changing relationship among chemical components is a vital aspect in chemistry. In this present manuscript, we put forward a new fractional-order delayed Brusselator chemical reaction model. By virtue
of contraction mapping principle, we investigate the existence and uniqueness of the solution of fractional-order delayed Brusselator chemical reaction model. With the aid of mathematical analysis technique, we consider the non-negativeness
of the solution of the fractional-order delayed Brusselator chemical reaction model. Making use of the theory of fractional-order dynamical system, we explore the stability and Hopf bifurcation issue of the fractional-order delayed Brusselator
chemical reaction model. By designing a reasonable \(PD^\varsigma\) controller, we have availably controlled the time of emergence of Hopf bifurcation of the fractional-order delayed Brusselator chemical reaction model. A sufficient criterion
guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled delayed Brusselator chemical reaction model is set up. Computer simulations are implemented to validate the theoretical findings. The derived
fruits of this manuscript have great theoretical significance in controlling the concentrations of chemical substances.
