Stability analysis for fractional order advection–reaction diffusion system

2019 ◽  
Vol 521 ◽  
pp. 737-751 ◽  
Author(s):  
Hasib Khan ◽  
J.F. Gómez-Aguilar ◽  
Aziz Khan ◽  
Tahir Saeed Khan
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System

Mathematical and computational studies of fractional reaction-diffusion system modelling predator-prey interactions

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Kolade M. Owolabi ◽  
Edson Pindza
Keyword(s):  
Stability Analysis ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
System Modelling ◽  
Computational Studies ◽  
Mathematical Basis ◽  
Transform Method ◽  
Reaction Diffusion Systems ◽  
Fractional Reaction

Abstract This paper provides the essential mathematical basis for computational studies of space fractional reaction-diffusion systems, from biological and numerical analysis perspectives. We adopt linear stability analysis to derive conditions on the choice of parameters that lead to biologically meaningful equilibria. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. For the solution of the full reaction-diffusion system modelled by the fractional partial differential equations, we introduced the Fourier transform method to discretize in space and advance the resulting system of ordinary differential equation in time with the fourth-order exponential time differencing scheme. Numerical results.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

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