Query: Brusselator

title: On the solution of time fractional dynamical model of Brusselator reaction diffusion system arising in chemical reactions

title: Snaking branches of planar BCC fronts in the 3D Brusselator
abstract: We present results of the application of the numerical continuation and bifurcation package pde2path to the 3D Brusselator model, focusing on snaking branches of planar fronts between body centered cubes (BCCs) and the spatial homogeneous solution, and on planar fronts between BCCs and tubes (also called prisms) These solutions also yield approximations of localized BCCs, and of BCCs embedded in a background of tubes (or vice versa) Additionally, we compute some moving fronts between lamellas and tubes. To give some theoretical background, and to aid the numerics for the full system, we use the Maxwell points for the cubic amplitude system over the BCC lattice.

title: High Order Analysis of Canard Explosion in the Brusselator Equations
abstract: The aim of this paper is to obtain a high order approximation of the canard explosion in the Brusselator equations. This classical chemical system has been extensively studied but, until now, only

title: Multistability and Stochastic Phenomena in the Distributed Brusselator Model
abstract: An influence of random disturbances on the pattern formation in reaction diffusion systems is studied. As a basic model, we consider the distributed Brusselator with one spatial variable. A coexistence of the stationary nonhomogeneous spatial structures in the zone of Turing instability is demonstrated. A numerical parametric analysis of shapes, sizes of deterministic pattern attractors, and their bifurcations is presented. Investigating the corporate influence of the multistability and stochasticity, we study phenomena of noise induced transformation and generation of patterns.

title: Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator.
abstract: Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non equilibrium steady state (NESS) In reality, these processes take place in finite systems containing a finite number of molecules. In such systems, a NESS can be reached with the help of an externally driven pump for which we introduce a simple model. The crucial parameters are the pumping rate and the finite size of the chemical reservoir. We apply this model to a simple biochemical oscillator, the Brusselator, and quantify the performance using the number of coherent oscillations. As a surprising result, we find that higher precision can be achieved with finite size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.

title: Numerical modeling of three dimensional Brusselator reaction diffusion system
abstract: In many mathematical models, positivity is one of the attributes that must be possessed by the continuous systems. For instance, the unknown quantities in the Brusselator reaction diffusion model represent the concentration of two reactant species. The negative values of concentration produced by any numerical methods is meaningless. This work is concerned with the investigation of a novel unconditionally positivity preserving finite difference (FD) scheme to be used for the solution of three dimensional Brusselator reaction diffusion system. Von Neumann stability method and Taylor series expansion is applied to verify unconditional stability and consistency of the proposed FD scheme. Results are compared against well known forward Euler FD scheme and some results reported in the literature.In many mathematical models, positivity is one of the attributes that must be possessed by the continuous systems. For instance, the unknown quantities in the Brusselator reaction diffusion model represent the concentration of two reactant species. The negative values of concentration produced by any numerical methods is meaningless. This work is concerned with the investigation of a novel unconditionally positivity preserving finite difference (FD) scheme to be used for the solution of three dimensional Brusselator reaction diffusion system. Von Neumann stability method and Taylor series expansion is applied to verify unconditional stability and consistency of the proposed FD scheme. Results are compared against well known forward Euler FD scheme and some results reported in the literature.

title: Turing Instability of Brusselator in the Reaction Diffusion Network
abstract: Turing instability constitutes a universal paradigm for the spontaneous generation of spatially organized patterns, especially in a chemical reaction. In this paper, we investigated the pattern dynamics of Brusselator from the view of complex networks and considered the interaction between diffusion and reaction in the random network. After a detailed theoretical analysis, we obtained the approximate instability region about the diffusion coefficient and the connection probability of the random network. In the meantime, we also obtained the critical condition of Turing instability in the network organized system and found that how the network connection probability and diffusion coefficient affect the reaction diffusion system of the Brusselator model. In the end, the reason for arising of Turing instability in the Brusselator with the random network was explained. Numerical simulation verified the theoretical results.

title: Bifurcation Behaviors of Steady State Solution to a Discrete General Brusselator Model
abstract: We study the local and global bifurcation of nonnegative nonconstant solutions of a discrete general Brusselator model. We generalize the linear u in the standard Brusselator model to the nonlinear f(u) Assume that f C([0, [0, is a strictly increasing function, and f'(f 1(a) (0, Taking b as the bifurcation parameter, we obtain that the solution set of the problem constitutes a constant solution curve and a nonconstant solution curve in a small neighborhood of the bifurcation point

title: APPROXIMATE SOLTUIONS OF CHEMICAL REACTION DIFFUSION BRUSSELATOR SYSTEM USING NEW ITERATIVE METHOD
abstract: This article, presents the approximate solutions of Chemical Reaction Diffusion Brusselator system and Coupled Schrodinger Korteweg de Vries equation by a reliable algorithm of New Iterative Method. New Iterative Method is an improvement with regard to its accuracy and rapid convergence. Numerical results show that the proposed method is reliable and efficient. The accuracy of the method increases with increase in the number of iterations.

title: Computational Scheme for the Time Fractional Reaction Diffusion Brusselator Model
abstract: In this work, we present an adaptation of a new look of the fractional Maclaurin series to study the time fractional reaction diffusion Brusselator system. Also, we give a description of implementing the suggested numerical scheme to provide a supportive approximation solution to the time fractional Brusselator. We study the physical shape of the depicted solution upon changing the order of the fractional derivative and concluding some results. The analysis conducted in this work is supported by 2D 3D plots. Finally, we discuss other numerical techniques that has been used in obtaining simulated solutions for the fractional Brusselator model.