  We hereby develop the theory of Turing instability for reaction-diffusion
systems defined on complex networks assuming finite propagation. Extending to
networked systems the framework introduced by Cattaneo in the 40's, we remove
the unphysical assumption of infinite propagation velocity holding for
reaction-diffusion systems, thus allowing to propose a novel view on the fine
tuning issue and on existing experiments. We analytically prove that Turing
instability, stationary or wave-like, emerges for a much broader set of
conditions, e.g., once the activator diffuses faster than the inhibitor or even
in the case of inhibitor-inhibitor systems, overcoming thus the classical
Turing framework. Analytical results are compared to direct simulations made on
the FitzHugh-Nagumo model, extended to the relativistic reaction-diffusion
framework with a complex network as substrate for the dynamics.
