Flip and generalized flip bifurcations of a two-dimensional discrete-time chemical model

Naik, Parvaiz Ahmad; Eskandari, Zohreh; Shahraki, Hossein Eskandari

doi:10.53391/mmnsa.2021.01.009

Cited by 27 publications

(10 citation statements)

References 26 publications

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“…by Euler's forward formula, where α 1 , α 2 are positive constants, x and y, respectively, represent fructose-6-phosphate and adenosine diphosphate. Naik et al [18] have explored the bifurcations of the following discrete chemical model:…”

Section: Review Of Literature and Statement Of The Problemmentioning

confidence: 99%

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

2022

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The local dynamics, chaos, and bifurcations of a discrete Brusselator system are investigated. It is shown that a discrete Brusselator system has an interior fixed point P 1 , r if r > 0 . Then, by linear stability theory, local dynamical characteristics are explored at interior fixed point P 1 , r . Furthermore, for the discrete Brusselator system, the existence of periodic points is investigated. The existence of bifurcations around an interior fixed point is also investigated and proved that the discrete Brusselator model undergoes hopf and flip bifurcations if r , h ∈ ℋℬ | P 1 , r = r , h , h = 2 − r and r , h ∈ ℱℬ | P 1 , r = r , h , h = 4 / 2 − r − r 2 − 4 r , respectively. The next feedback control method is utilized to stabilize the chaos that exists in the discrete Brusselator system. Finally, obtained results are verified numerically.

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Section: Review Of Literature and Statement Of The Problemmentioning

confidence: 99%

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

2022

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“…Chaos theory describes the behavior of certain dynamical systems whose state evolves with time and are highly sensitive to initial conditions. Because of the complexity of chaotic behavior in dynamical systems, it finds applications in a variety of fields, such as science, technology and medicine [8,9,10,11,12,13,14]. Studying chaotic systems can be a very valuable endeavor.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional fractional system with the stability condition and chaos control

Gholami

Ghaziani

Eskandari

2022

mmnsa

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A three-dimensional system is introduced in this paper and its local stability is analyzed. Our study establishes the validity and uniqueness of the linear feedback control for the proposed system and proves its existence and uniqueness. The numerical simulation algorithm described by Atanackovic and Stankovic is finally applied. The analytical results are analyzed and the dynamics of the system are explored in more detail.

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“…We have also the so-called Atangana-Baleanu fractional operator and the Caputo-Fabrizio derivative which are known as the fractional operators with non-singular kernels [4,5]. These singular and non-singular derivatives appear in many papers with applications to physical modeling [2,6,7], biological modeling [8,9,10,11,12,13,14], sciences and engineering modeling [15,16,17,18,19], mathematical physics modeling [20,21,22,23,24,25,26], physics modeling [24,27] and others domains [28,29,30,31,32]. The field of fractional calculus is interesting but there also exist many questions without responses.…”

Section: Introductionmentioning

confidence: 99%

Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

Sene

2022

mmnsa

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In this paper, we consider the constructive equations of the fractional second-grade fluid. The considered fluid model is described by the Caputo derivative. The problem consists to determine the exact analytical solution using the Laplace transform method. The influence of the order of the used fractional operator has been presented in this paper. We also analyze the influence of the Prandtl number in the dynamics of the temperature distribution according to the variation of the order of the Caputo derivative. The impact of the second-grade parameter and the Grashof number in the dynamics of the velocity has been presented and discussed. The influences of the parameters used in the modeling have been interpreted in terms of a fractional context. In general, it is shown that the order of the fractional operator influences the diffusivity of the considered fluid. This influence can cause an increase or decrease in the temperature and velocity distributions. The main findings of the paper have been illustrated using the graphical representations of the considered distributions according to the order of the fractional operator.

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Flip and generalized flip bifurcations of a two-dimensional discrete-time chemical model

Cited by 27 publications

References 26 publications

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

Three-dimensional fractional system with the stability condition and chaos control

Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

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