Pattern formation in reaction diffusion models
is a topic of paramount importance which finds applications in distinct disciplinary contexts. According to the deterministic picture, partial differential equations are assumed to govern the evolution of the concentrations of interacting species. A small perturbation of a homogeneous fixed point can spontaneously amplify in a reaction diffusion system, as follow a symmetry breaking instability and eventually yield to asymptotically stable non homogeneous patterns, the celebrated Turing patterns. Traveling waves can also manifest as a byproduct of the instability. Beyond the deterministic scenario, single individual effects, stemming from the intimate discreteness of the analysed medium, prove crucial
by significantly modifying the mean-field predictions. The stochastic component of the microscopic dynamics can in particular induce the emergence of regular macroscopic patterns, in time and space, outside the region of deterministic instability. To gain insight
into the role of fluctuations and eventually work out the conditions for the emergence of stochastic patterns, one can operate under the linear noise approximations scheme. Starting from this setting, I will discuss the dynamics of (stochastic) reaction diffusion models defined on a complex (random and/or scale free) network. The linear noise approximation scheme will be adapted to network based applications and the condition for stochåastic waves and Turing like patterns obtained. Numerical simulations will be also performed to confirm the adequacy of the theory.