Linear and nonlinear information flow in spatially extended systems - art.no. 056201

Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information tra nsport in these systems can be characterized in terms of the propagation ve locity of perturbations V-p. A linear stability analysis is sufficient to c apture all the relevant aspects associated to propagation of infinitesimal disturbances. In particular, this analysis gives the propagation velocity V -L of infinitesimal errors. If linear mechanisms prevail on the nonlinear o nes V-p = V-L. On the contrary, if nonlinear effects an predominant finite amplitude disturbances can eventually propagate faster than infinitesimal o nes (i.e., V-p > V-L). The finite size Lyapunov exponent can be successfull y employed to discriminate the linear or nonlinear origin of information fl ow. A generalization of the finite size Lyapunov exponent to a comoving ref erence frame allows us to state a marginal stability criterion able to prov ide V-p both in the linear and in the nonlinear case. Strong analogies are found between information spreading and propagation of fronts connecting st eady states in reaction-diffusion systems. The analysis of the common chara cteristics of these two phenomena leads to a better understanding of the ro le played by linear and nonlinear mechanisms for the flow of information in spatially extended systems.