Bifurcations and pattern formation in a generalized Lengyel–Epstein reaction–diffusion model

Mansouri, Djamel; Abdelmalek, Salem; Bendoukha, Samir

doi:10.1016/j.chaos.2019.109579

Cited by 8 publications

(3 citation statements)

References 17 publications

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“…holds. Therefore, the equilibrium point (u * , v * ) of system ( 6) is locally asymptotically stable under the condition (10) since det(J * ) is positive for all parameter values (see (8)). The analysis given above leads to the stability conditions of the system without diffusion as follows.…”

Section: Stability Analysis Of System (1)mentioning

confidence: 99%

“…In [1], some properties of non-homogeneous equilibrium solutions of generalized Lengyel-Epstein system was analyzed and sufficient conditions for global asymptotic stability of equilibrium solution was reached by Abdelmalek and et al In [10], the existence of diffusion driven instability and stability conditions of periodic solutions for generalized Lengyel-Epstein model were proved, besides some numerical results were presented by Mansouri and coauthors. In [16], sufficient conditions for Hopf and Bautin bifurcations of the generalized Lengyel-Epstein system involving a system of ordinary differential equations below…”

Section: Introductionmentioning

confidence: 99%

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Patern Formation and Diffusion-Driven Instability of a Modified Lengyel-Epstein Model

MEYVACI,

MERDAN,

Yafia

2023

Preprint

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We consider a modified Lengyel-Epstein model that is covered by a system of reaction diffusion equations and investigate the sufficient conditions on parameters of the model at which the diffusion driven instability occurs. We perform numerical simulations to support and extend the theoretical findings. Analytical results and numerical simulations show that the modified Lengyel-Epstein system with positive initial and non-flux boundary conditions presents Turing patterns under some conditions on its parameters. Lengyel–Epstein system 2008 MSC: 35K57, 35K50, 92D25, 92C15 (2000 is the default)

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Section: Stability Analysis Of System (1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Patern Formation and Diffusion-Driven Instability of a Modified Lengyel-Epstein Model

MEYVACI,

MERDAN,

Yafia

2023

Preprint

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show abstract

“…(40) and (41) along with Eq. (39) and putting in the Eqs. (35) and (36), and get the system of equations.…”

Section: Application To Lengyel-epstein Reaction Diffusion Systemmentioning

confidence: 99%

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

Ahmed,

Baber,

Iqbal

et al. 2023

Sci Rep

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In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction–diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reactionâ€ “diffusion model which considered for the first time analytically to explore the different abundant families of solitary wave structures. These exact solitary wave solutions are obtained by applying the generalized Riccati equation mapping method. The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions also emerged during the derivation. In the Lengyel-Epstein system, solitary waves can propagate at various rates. The harmony of the system’s diffusive and reactive effects frequently governs the speed of a single wave. Solitary waves can move at a variety of speeds depending on the factors and reaction kinetics. To show their physical behavior, the 3D and their corresponding contour plots are drawn for the different values of constants.

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Spatiotemporal complexity in a diffusive Brusselator model

Chen

et al. 2021

J Math Chem

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Bifurcations and pattern formation in a generalized Lengyel–Epstein reaction–diffusion model

Cited by 8 publications

References 17 publications

Patern Formation and Diffusion-Driven Instability of a Modified Lengyel-Epstein Model

Patern Formation and Diffusion-Driven Instability of a Modified Lengyel-Epstein Model

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

Spatiotemporal complexity in a diffusive Brusselator model

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