Analysis of instabilities and pattern formation in time fractional reaction-diffusion systems

2009/12/08 by Datsko, B. Y., Gafiychuk, V. V.
#Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)

paper · doi:10.48550/arxiv.0912.1500

Abstract

We analyzed conditions for Hopf and Turing instabilities to occur in two-component fractional reaction-diffusion systems. We showed that the eigenvalue spectrum and fractional derivative order mainly determine the type of instability and the dynamics of the system. The results of the linear stability analysis are confirmed by computer simulation of the model with cubic nonlinearity for activator variable and linear dependance for the inhibitor one. It is shown that pattern formation conditions of instability and transient dynamics are different than for a standard system. As a result, more complicated pattern formation dynamics takes place in fractional reaction-diffusion systems.

Related

• Mathematical modeling of pattern formation in sub- and supperdiffusive reaction-diffusion systems
• Nonlinear oscillations and stability domains in fractional reaction-diffusion systems
• Tools for stability analysis of fractional reaction diffusion systems
• A new instability framework in 2-component reaction-diffusion systems
• Turing Instabilities and Patterns Near a Hopf Bifurcation