Right Type Departmental Bulletin Paper

We show that Turing instability can lead oscillatory reaction-diffusion $(\mathrm{R}\mathrm{D}) $ systems to spatiotemporal chaos instead of spa-tially periodic steady states. Similar onset of chaos was discov-ered in an equation that describes seismic waves (called Niko-laevskii turbulence) and observed experimentally in convective systems (called soft-mode turbulence). We demonstrate that a certain class of oscillatory RD sys-tems are reduced to an extended complex Ginzburg-Landau equation, whose uniformly oscillating solution possesses not 1485 2006 107-109 107 only Benjamin-Feir criticality but Turing criticality [1]. In the neighborhood of a codimension-two point of these criticality, we derive a phase equation equivalent to the seismic equation [2]. We also present numerical studies of reduced equations and a three-component RD model in this regime [2] [3] [6]. The numerical results support our argument and show robustness of this type of spatiotemporal chaos [6]. Finally, we derive critical exponents of chaotic fluctuations and study bifurcation scenario to this chaos $[4][5] $. References 1. Dan Tanaka and Yoshiki Kuramot