Turing instability leads oscillatory systems to spatiotemporal chaos

Abstract

We present that Turing instability can lead oscillatory reaction-diffusion (RD) systems to spatiotemporal chaos instead of spatially periodic steady states. Similar onset of spatiotemporal chaos was discovered in an equation describing seismic waves. We demonstrate that the seismic equation can be derived from a certain class of oscillatory RD systems in the neighborhood of a codimension-two Turing-Benjamin-Feir point. Also, we show numerical studies of reduced equations and discuss robustness of this spatiotemporal chaos.