Turing’s Diffusive Threshold in Random Reaction-Diffusion Systems

Diffusive stability of oscillations in reaction-diffusion systems

We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations decay algebraically with the diffusive rate t−n/2 in space dimension n. We also compute the leading order term in the asymptotic expansion of the solution, ...

Diffusive mixing of periodic wave trains in reaction-diffusion systems

We consider reaction-diffusion systems on the infinite line that exhibit a family of spectrally stable spatially periodic wave trains u0(kx− ωt; k) that are parameterized by the wave number k. We prove stable diffusive mixing of the asymptotic states u0(kx + φ±; k) as x → ±∞ with different phases φ− 6= φ+ at infinity for solutions that initially converge to these states as x → ±∞. The proof is ...

Random channel kinetics for reaction-diffusion systems

A random channel approach is developed for reaction-diffusion processes in disordered systems. Although the starting point of our research is the kinetic study of the decay and preservation of marine organic carbon, our approach can be used for describing other disordered kinetic catalytic processes with random pathways. We consider a generic catalytic mechanism with two species: a) a catalyst,...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Diffusion-Driven Instability in Reaction Diffusion Systems

For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press