Bifurcation Dynamics and Control Mechanism of a Fractional-Order Delayed Brusselator Chemical Reaction Model

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 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.

Further Insight into Bifurcation and Hybrid Control Tactics of a Chlorine Dioxide-Iodine-Malonic Acid Chemical Reaction Model Incorporating Delays

“…In view of Lemma 1 of Das et al [18], one gains u 1 (t + ⋆ ) = 0, which is a contradiction (see (12)). So u 1 (t) ≥ 0 for t ≥ t 0 .…”

“…Hopf bifurcation driven by delay is an significant dynamical peculiarity in nonlinear delayed differential models [6][7][8][9][10][11][12][13][14][15][16]. In chemistry, Hopf bifurcation driven by delay can availably characterize the transformation relationship of the concentration of different chemical substances.…”

Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System

“…The qualitative behavior is explored for proposed model and our investigation proves the consistency preserving properties. Taking into account the fact that the fractional-order chemical reaction systems have the potential to improve our understanding of a wide range of chemical processes and to provide new insights into the behavior and control of these systems [29][30][31][32][33][34], we will consider a fractional-order counterpart of the system (3) for our future investigation.…”

Complex dynamics analysis and feedback control for a memristive switched chaotic system

“…To enrich the theory of chaotic systems and improve the complexity of chaotic systems, many scholars have done a lot of research work to construct new systems. Various types of new chaotic systems have been proposed, such as hyperchaotic systems [6], conservative chaotic systems [7], hidden chaotic systems [8][9][10][11], fractional order systems [12][13][14], and time delay systems [15,16]. As a new type of component, memristors can be incorporated into nonlinear systems to enhance their nonlinear characteristics.…”