Linear and nonlinear information flow in spatially extended systems

Details Linear and nonlinear information flow in spatially extended systems Linear and nonlinear information flow in spatially extended systems

2000-11-23

arxiv.org/abs/nlin/0011044v2

Physical Review E 63, 056201 (2001)

Nonlinear Sciences

Chaotic Dynamics

14 RevTeX pages with 13 eps figures, title/abstract changed minor changes in the text accepted for publication on PRE

Scientific paper

10.1103/PhysRevE.63.056201

Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be characterized in terms of the propagation velocity of perturbations $V_p$. A linear stability analysis is sufficient to capture 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 ones $V_p = V_L$. On the contrary, if nonlinear effects are predominant finite amplitude disturbances can eventually propagate faster than infinitesimal ones (i.e. $V_p > V_L$). The finite size Lyapunov exponent can be successfully employed to discriminate the linear or nonlinear origin of information flow. A generalization of finite size Lyapunov exponent to a comoving reference frame allows to state a marginal stability criterion able to provide $V_p$ both in the linear and in the nonlinear case. Strong analogies are found between information spreading and propagation of fronts connecting steady states in reaction-diffusion systems. The analysis of the common characteristics of these two phenomena leads to a better understanding of the role played by linear and nonlinear mechanisms for the flow of information in spatially extended systems.

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