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

Din, Qamar; Saeed, Umer

doi:10.46793/match.90-1.151d

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…Ameen [1] recently examined a biochemical reaction system to discuss its numerous algebraic surfaces, exponential factors, and lack of integration. In recent research on oscillatory solutions and chaos, a chemical reaction involving two species [6] has been considered. In 2022, Din [7] examined a three-dimensional chaotic system without using its eigenvalues to determine the existence of Hopf bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

Marwan,

Xiong,

Han

et al. 2023

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This research examines a chaotic chemical reaction system based on the variation of the Lorenz system. This study demonstrates that although the first phase portraits of the chemical models under consideration and the Lorenz models are comparable, they do not fully follow all the features of the Lorenz system. Questions about the existence of fractals in systems based on chemical reactions are addressed in the current work. Moreover, we have worked on the hidden information inside in each wings of a chaotic system generated through fractal process, for the first time, with the aid of basin for fractals. Additionally, we looked closely at the dynamics of the model across the basin, which revealed additional details regarding the existence of hidden and cyclic attractors inside each wing. We also produced multi-wings for system (1) in the current study, demonstrating in a general manner that the number of cyclic attractors increase in a direct relation to the number of wings. Moreover, Julia approach is used to accomplish the work of multi-wings, whereas for searching cyclic attractors inside each extra wing, we have used fifteen million initial conditions and compiled them as a basin set. The data generated in this work is also provided within this paper for the ease of readers.

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Section: Introductionmentioning

confidence: 99%

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

Marwan,

Xiong,

Han

et al. 2023

match

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“…Overall, fractional order chemical reaction models are a powerful tool in the field of chemistry and related disciplines [23]. For further reading on mathematical models concerning chemical reactions in both continuous and discrete frameworks, the reader is encouraged to consult references [32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Codimension-One and Codimension-Two Bifurcations of a Fractional-Order Cubic Autocatalator Chemical Reaction System

Khan,

Din

2023

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This article delves into an investigation of the dynamic behavior exhibited by a fractional order cubic autocatalator chemical reaction model. Specifically, our focus lies on exploring codimension-one bifurcations associated with period-doubling bifurcation and Neimark-Sacker bifurcation. Additionally, we undertake an analysis of codimension-two bifurcations linked to resonances of the types 1:2, 1:3, and 1:4. To achieve these outcomes, we employ the normal form method and bifurcation theory. The results are presented through comprehensive numerical simulations, encompassing visual representations such as phase portraits, two-parameter bifurcation diagrams, and maximum Lyapunov exponents diagrams. These simulations aptly examine the behavior of a system governed by two distinct parameters that vary within a three-dimensional space. Furthermore, the simulations effectively illustrate the theoretical findings while providing valuable insights into the underlying dynamics.

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“…Wong and Ward [4] developed a hybrid asymptotic-numerical theory with respect to the effect of different types of localized heterogeneities on the existence, stability, and slow dynamics of spot patterns for the Schnakenberg reaction-diffusion model in a 2-D domain. Please refer to [5][6][7][8][9] for more dynamic results with respect to the chemical models.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Self-Organization Pattern of a Modified Brusselator Model

Chen¹

2023

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This paper reports the Hopf bifurcation and self-organization pattern of a modified Brusselator model. The model is a non-standard Brusselator model, it involves the nonlinear restraint term. For the non-diffusive model, we give the types of unique positive equilibrium. It is found that the unique positive equilibrium may be focus, node, or center and we establish their stability, respectively. Especially, there exists the spatial homogeneous Hopf bifurcation when the equilibrium is a center. The first Lyapunov number technique is applied to perform the direction of the spatial homogeneous Hopf bifurcation. In the sequel, the occurrence conditions of the Turing instability and the spatial inhomogeneous Hopf bifurcation are given for the diffusive model. Moreover, by using the normal form theory, we show that the Hopf bifurcation is supercritical or subcritical. Finally, the self-organization patterns induced by the Turing instability and periodic solutions resulting from the Hopf bifurcation are displayed by employing numerical simulations. Our theoretical predictions and numerical results reveal that the modified Brusselator model enjoys the temporal period oscillation and spatial oscillation due to the Hopf bifurcation and Turing instability, respectively. These results may help us to figure out the spatio-temporal dynamics of such modified Brusselator model.

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

Cited by 4 publications

References 31 publications

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

Codimension-One and Codimension-Two Bifurcations of a Fractional-Order Cubic Autocatalator Chemical Reaction System

Hopf Bifurcation and Self-Organization Pattern of a Modified Brusselator Model

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