Stability analysis for Selkov-Schnakenberg reaction-diffusion system

Noufaey, K.S. Al

doi:10.1515/math-2021-0008

Cited by 23 publications

(13 citation statements)

References 38 publications

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“…The final example solves the Schnackenberg equations where the parameters are chosen to be D u = 0.001 , D v = 0.1 , 0.003 , 2 = 0.7 , and = 0.06 inspired in part by [26]. The initial conditions are set as (21)…”

Section: Ddcpschnackenbergmentioning

confidence: 99%

A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners

2022

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The DD-CPM software library provides a set of tools for the discretization and solution of problems arising from the closest point method (CPM) for partial differential equations on surfaces. The solvers are built on top of the well-known PETSc framework, and are supplemented by custom domain decomposition (DD) preconditioners specific to the CPM. These solvers are fully compatible with distributed memory parallelism through MPI. This library is particularly well suited to the solution of elliptic and parabolic equations, including many reaction-diffusion equations. The software is detailed herein, and a number of sample problems and benchmarks are demonstrated. Finally, the parallel scalability is measured.

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Section: Ddcpschnackenbergmentioning

confidence: 99%

A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners

2022

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“…4.1.6 DDCPSchnackenberg. The final example solves the Schnackenberg equations where the parameters are chosen to be 𝐷 𝑢 = 0.001, 𝐷 𝑣 = 0.1, 𝛿 1 = 0.003, 𝛿 2 = 0.7, and 𝜆 = 0.06 inspired in part by [Noufaey 2021]. The initial conditions are set as…”

Section: Included Examplesmentioning

confidence: 99%

A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners

May¹,

Haynes²,

Ruuth³

2021

Preprint

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“…This method provides a comparison with the analytical solution to demonstrate the accuracy of analytical results. Some examples that use this method include the Selkov-Schnakenberg reaction-diffusion system [25], the BZ model [1], Nicholson's blowflies system [26], neural network systems [27], logistic equations with delays [12,[28][29][30], the Gray and Scott cubic autocatalytic system [6], viral infection models [11], and the foodlimited equation [31]. In general, all the researchers that have applied this method reported an extremely agreeable comparison between the theoretical ODE results and the numerical scheme of the PDE model.…”

Section: Introductionmentioning

confidence: 99%

Feedback Control for a Diffusive and Delayed Brusselator Model: Semi-Analytical Solutions

Alfifi

2021

Symmetry

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This paper describes the stability and Hopf bifurcation analysis of the Brusselator system with delayed feedback control in the single domain of a reaction–diffusion cell. The Galerkin analytical technique is used to present a system equation composed of ordinary differential equations. The condition able to determine the Hopf bifurcation point is found. Full maps of the Hopf bifurcation regions for the interacting chemical species are shown and discussed, indicating that the time delay, feedback control, and diffusion parameters can play a significant and important role in the stability dynamics of the two concentration reactants in the system. As a result, these parameters can be changed to destabilize the model. The results show that the Hopf bifurcation points for chemical control increase as the feedback parameters increase, whereas the Hopf bifurcation points decrease when the diffusion parameters increase. Bifurcation diagrams with examples of periodic oscillation and phase-plane maps are provided to confirm all the outcomes calculated in the model. The benefits and accuracy of this work show that there is excellent agreement between the analytical results and numerical simulation scheme for all the figures and examples that are illustrated.

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Stability analysis for Selkov-Schnakenberg reaction-diffusion system

Cited by 23 publications

References 38 publications

A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners

A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners

A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners

Feedback Control for a Diffusive and Delayed Brusselator Model: Semi-Analytical Solutions

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