Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

2010 ◽  
Vol 70 (7) ◽  
pp. 2150-2185 ◽  
Author(s):  
Akif Ibragimov ◽  
Laura Ritter ◽  
Jay R. Walton
Keyword(s):  
Stability Analysis ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System

A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

2010 ◽  
Vol 20 (05) ◽  
pp. 731-756 ◽  
Author(s):  
VERÓNICA ANAYA ◽  
MOSTAFA BENDAHMANE ◽  
MAURICIO SEPÚLVEDA
Keyword(s):  
Weak Solution ◽  
Numerical Analysis ◽  
Numerical Scheme ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence Of Weak Solutions ◽  
Early Tumor ◽  
Volume Method

We consider a reaction–diffusion system of 2 × 2 equations modeling the spread of early tumor cells. The existence of weak solutions is ensured by a classical argument of Faedo–Galerkin method. Then, we present a numerical scheme for this model based on a finite volume method. We establish the existence of discrete solutions to this scheme, and we show that it converges to a weak solution. Finally, some numerical simulations are reported with pattern formation examples.

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.

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