Turing Diffusion Instability Band

The Turing instability (or diffusion-driven instability) is a phenomenon in which a system that is stable to homogeneous perturbations becomes unstable to spatially inhomogeneous perturbations when diffusion is introduced. Specifically, we study a linear two-species reaction-diffusion system. Find the spatial modes that diffusion destabilizes despite stable local reactions.

Experiment: Changing Wavenumbers and Diffusivity

In this experiment, we explore how changing the diffusion ratio and the spatial mode impacts stability. Follow these steps in the interactive Turing Diffusion Instability Band module:

1. Set the Diffusivity ratio control to 16.
2. Set the Squared wavenumber control to 1/4. Observe the Mode stability indicator showing "Growing".
3. Change the Squared wavenumber to 0. The system behaves like the homogeneous case without diffusion, and the mode decays.
4. Change the Diffusivity ratio to 9 and the Squared wavenumber to 1/3. You will find that the system reaches a "Critical touch" with a maximum growth rate of exactly 0.
5. Finally, change the Diffusivity ratio to 1. With equal diffusion, the system cannot destabilize, and there is "No unstable band" regardless of the wavenumber.