Subcritical Turing patterns in hyperbolic models with cross–diffusion

This paper focuses on the role of hyperbolicity on pattern formation in the subcritical regime for a class of hyperbolic models with cross-diffusion. A weakly nonlinear analysis up to the fifth order is employed to describe the time evolution of the pattern amplitude close to the instability threshold. The effects of the inertial times on the pattern formation as well as on the transient subcritical regime are investigated, both analitically and numerically, in the case of the hyperbolic Schnakenberg model.