Bifurcation dynamics in a fractional-order oregonator model including time delay

Xu, Changjin; Economics, China; Zhang, Wei; Aouiti, Chaouki; Liu, Zixin; Li, Peiluan; Yao, Lingyun

doi:10.46793/match.87-2.397x

Cited by 8 publications

(6 citation statements)

References 20 publications

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“…4 Bifurcation exploration of model (4) In this section, we will investigate the stability and Hopf bifurcation of model ( 4). Obviously, model (4) has unique positive equilibrium points…”

Section: Existence and Uniqueness Non-negativeness Of Solutionmentioning

confidence: 99%

“…5 Bifurcation control of model ( 4) via P D ς controller In this section, we are to apply PD ς controller to control the Hopf bifurcation of model (4). The PD ς controller is designed as follows:…”

Section: By (20) We Derivementioning

confidence: 99%

“…Kapral [3] discussed the complex dynamical phenomena of a discrete chemical reaction model. Xu et al [4] explored the limit cycle of a fractional-order delayed Oregonator model. Xu et al [5] revealed the effect of delay on the bifurcation of a fractionalorder coupled Oregonator model.…”

Section: Introductionmentioning

confidence: 99%

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

Xu¹,

Mu²,

Liu³

et al. 2022

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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.

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“…4 Bifurcation exploration of model (4) In this section, we will investigate the stability and Hopf bifurcation of model ( 4). Obviously, model (4) has unique positive equilibrium points…”

Section: Existence and Uniqueness Non-negativeness Of Solutionmentioning

confidence: 99%

Section: By (20) We Derivementioning

confidence: 99%

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

Xu¹,

Mu²,

Liu³

et al. 2022

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“…Here we would like to point out that all the works mentioned above (see, [11,12,36]) focused on integer-order chemical systems. Studies in recent decades manifest that the fractional-order dynamical model has been regarded as a more efficient implementation to characterize practical phenomena than the conventional integer-order ones since the fractionalorder dynamical model can display immense advantages in keeping memory and hereditary properties of a lot of materials and change process [15,19,22,32,34,37,39]. Nowadays, fractional-order dynamical models have been widely applied in many fields such as neural networks, control engineering, physical waves, biology, chemistry, economics and so forth [20,32,41].…”

Section: Geysermans and Nicolismentioning

confidence: 99%

Bifurcation Anti-Control Tactics of a Fractional-Order Stable Chemical Reaction System

Liu¹

2022

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Establishing suitable differential dynamical models to describe the real natural phenomenon in chemistry and physics has become a very hot topic in nowadays society. In this present research, we deal with a fractional-order chemical reaction system. Taking advantage of the fixed point theorem, we prove the existence and uniqueness of the fractional-order chemical reaction system. Using the inequality skill, we prove the non-negativeness of the fractional-order chemical reaction system. By applying a suitable function, we prove the uniform boundedness of the solution to the fractional-order chemical reaction system. With the aid of a hybrid controller including state feedback and parameter perturbation, we discuss the Hopf bifurcation anti-control issue of the fractional-order stable chemical reaction system. A novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation of the involved fractional-order stable chemical reaction system is set up. The study manifests that the delay in the hybrid controller plays a vital role in stabilizing the system and controlling the occurrence of Hopf bifurcation of the fractional-order stable chemical reaction system. In order to validate the derived key conclusions, MATLAB simulations are executed and bifurcation plots are given. The obtained results of this article have momentous theoretical guiding value in controlling the chemical compositions. The exploration idea can also be utilized to investigate the bifurcation control and bifurcation anti-control problems in lots of other fractional-order differential systems in numerous disciplines.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Mu¹,

Xu²,

Liu³

et al. 2023

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Delayed differential equation is an important tool to describe the interaction of different chemical substance in chemistry. In this present research, we set up a novel chlorine dioxide-iodine-malonic acid chemical reaction model incorporating delays. The peculiarity of solution and Hopf bifurcation of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model are explored. Firstly, the existence and uniqueness is investigated via fixed point theorem. Secondly, the non-negativeness of solution is studied via some proper mathematical inequality shills. Thirdly, the stability and bifurcation of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model are analyzed. The influence of delay on the delayed chlorine dioxide-iodine-malonic acid chemical reaction model is uncovered. Fourthly, Hopf bifurcation control issue of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model is studied via two hybrid controllers. To check the soundness of acquired key assertions, Matlab simulations are executed. The gained assertions of this research are completely novel and possess tremendous theoretical value in maintaining the balance of the concentrations of chlorine dioxide, iodine in chemistry.

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Bifurcation dynamics in a fractional-order oregonator model including time delay

Cited by 8 publications

References 20 publications

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

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

Bifurcation Anti-Control Tactics of a Fractional-Order Stable Chemical Reaction System

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

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