Oscillatory instability in super-diffusive reaction -- diffusion systems: fractional amplitude and phase diffusion equations

TL;DR

This paper derives and analyzes fractional amplitude and phase diffusion equations to understand oscillatory instability in super-diffusive reaction-diffusion systems near a Hopf bifurcation, combining analytical and numerical approaches.

Contribution

It introduces fractional analogues of key equations in reaction-diffusion systems and explores their solutions, advancing understanding of super-diffusive oscillatory behaviors.

Findings

Derived fractional Ginzburg-Landau and Kuramoto-Sivashinsky equations

Analyzed analytical solutions of the fractional equations

Numerically studied the behavior of solutions near bifurcation

Abstract

Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical solutions are studied.