Global structure in spatiotemporal chaos of the Matthews-Cox equations

We find that an amplitude death state and a spatiotemporally chaotic state coexist spontaneously in the Matthews-Cox equations and this coexistence is robust. Although the entire system is far from equilibrium, the domain wall between the two states is stabilized by a negative-feedback effect due to a conservation law. This is analogous to the phase separation in conserved systems that exhibit spinodal decompositions. We observe similar phenomena also in the Nikolaevskii equation, from which the Matthews-Cox equations were derived. A Galilean invariance of the former equation corresponds to the conservation law of the latter equations.