Tracking Unstable Turing Patterns through Mixed-Mode Spatiotemporal Chaos

A method is presented for stabilizing and tracking unstable Turing patterns in reaction-diffusion systems. The Gray-Scott model is used to simulate a chemical system exhibiting spatiotemporal chaos arising from the interaction between Turing and Hopf bifurcations. The local behavior of the unstable pattern is first approximated with a single-input, single-output linear model constructed from a time series. A recursive control algorithm is then used to stabilize and track the unstable pattern by monitoring a single point in space and making small adjustments to a global parameter.