Heterogeneity induces spatiotemporal oscillations in 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, ...

Nonlinear oscillations and stability domains in fractional reaction-diffusion systems

We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It ...

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

Transient spatiotemporal chaos is extensive in three reaction-diffusion networks.

Extensive (asymptotic) spatiotemporal chaos is comprised of statistically similar subsystems that interact only weakly. A systematic study of transient spatiotemporal chaos reveals extensive system behavior in all three reaction-diffusion networks for various boundary conditions. The Lyapunov dimension, the sum of positive Lyapunov exponents, and the logarithm of the transient lifetime grow lin...