Diffusion-Induced Chaos in Reaction Systems

Temporal chaos versus spatial mixing in reaction-advection-diffusion systems.

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of...

Cross-diffusion Induced Instability and Stability in Reaction-diffusion Systems

In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize a uniform equilibrium which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize a uniform equilibrium which...

Chaos and Arnold Diffusion in Dynamical Systems

Abs~act -Chaotic motion refers to complicated trajectories in dynamical systems. It occurs even in deterministic systems governed by simple differential equations and its presence has been experimentally verified for many systems in several disciplines.-A technique-due to Melnikov provides an analytical tool for measuring chaos caused by horseshoes in certain systems.. The .phenomenon .of .,Amo...

Chaotic mixing induced transitions in reaction-diffusion systems.

We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the rate of the chemical reaction. When the stirring is fast localized perturbations decay towards a spatially homogeneous state. When the stirring is slow (or fa...

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