Cross-diffusion in the Templator model of chemical self-replication

For the Templator model of chemical self-replication, we consider the effect of cross-diffusion in pattern formation. Although other chemical systems with cross-diffusion have been reported, we are the first to obtain exact relations between the relevant parameters for the Poincaré–Adronov–Hopf and Turing bifurcations. Moreover, for the simplest case, we obtain analytical expressions in parameter space for the bifurcation curves and the Turing–PAH codimension two point.