Numerical Investigation of Chemical Schnakenberg Mathematical Model

Abstract

Schnakenberg model is known as one of the influential model used in several biological processes. The proposed model is an autocatalytic reaction in nature that arises in various biological models. In such kind of reactions, the rate of reaction speeds up as the reaction proceeds. It is because when a product itself acts as a catalyst. In fact, model endows fractional derivatives that got great advancement in the investigation of mathematical modeling with memory effect. Therefore, in the present paper, the authors develop a scheme for the solution of fractional order Schnakenberg model. The proposed model describes an auto chemical reaction with possible oscillatory behavior which may have several applications in biological and biochemical processes. In this work, the authors generalized the concept of integer order Schnakenberg model to fractional order Schnakenberg model. We provided the approximate solution for the underlying generalized nonlinear Schnakenberg model in the sense of Caputo differential operator via Laplace Adomian decomposition method (LADM). Furthermore, we established the general scheme for the considered model in the form of infinite series by the aforementioned technique. The consequent results obtained by the proposed technique ensure that LADM is an effective and accurate techniques to handle nonlinear partial differential equations as compared to the other available numerical techniques. Finally, the obtained numerical solution is visualized graphically by MATLAB to describe the dynamics of desired solution.

Chaotic dynamics of the fractional order Schnakenberg model and its control

“…A chemical Schnakenberg model was investigated [23], which depicts autochemical processes with rhythmic behavior that may have various biological and biochemical applications. A variable-order space-time fractional reaction-diffusion Schnakenberg model's numerical solutions were studied in [15].…”

“…A variable-order space-time fractional reaction-diffusion Schnakenberg model's numerical solutions were studied in [15]. In addition,the Schnakenberg model was described in [23,29,28], where a variety of numerical methods were employed to get approximations of solutions.…”

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

“…Liu et al [9] have developed the bifurcation analysis of the aforementioned model. Khan et al [10] have established a scheme for the solution of the fractional order Schnackenberg reaction-diffusion system. Numerical explorations have been applied to analyze the pattern formations of the model in the research article cited in [11].…”

Analytical Approximation of Brusselator Model via LADM

“…Describing such self-organization in physical systems is essential for the sake of understanding the physical and biological processes. In the last few decades, nonlinear chemical applications with di usion reactions under PDEs have been studied analytically and numerically, for instance, the pellet model [2], the reversible Selkov model [3], the Brusselator model [4], the Schnackenberg model [5] and the Belousov-Zhabotinsky (BZ) reaction [6]. In addition, the di usive nonlinear models have a large number of practical applications in several elds of applied mathematics.…”