Finite Wavelength Instabilities in a Slow Mode Coupled Complex Ginzburg-Landau Equation

In this letter, we discuss the effect of slow real modes in reaction-diffusion systems close to a supercritical Hopf bifurcation. The spatio-temporal effects of the slow mode cannot be captured by traditional descriptions in terms of a single complex Ginzburg-Landau equation (CGLE). We show that the slow mode coupling to the CGLE, introduces a novel set of finite-wavelength instabilities not present in the CGLE. For spiral waves, these instabilities highly effect the location of regions for convective and absolute instability. These new instability boundaries are consistent with transitions to spatio-temporal chaos found by simulation of the corresponding coupled amplitude equations.