Linear and nonlinear information flow in spatially extended systems

Abstract

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.

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

References in corpus (3)

• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Subdiffusive fluctuations of "pulled" fronts with multiplicative noise
• Transition to Stochastic Synchronization in Spatially Extended Systems

Cited by in corpus (11)

• Front propagation into unstable states
• The origin of diffusion: the case of non chaotic systems
• On the relationship between directed percolation and the synchronization transition in spatially extended systems
• Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
• Stable chaos in fluctuation driven neural circuits
• Nonlinearly driven transverse synchronization in coupled chaotic systems
• Characteristic distribution of finite-time Lyapunov exponents for chimera states
• On finite-size Lyapunov exponents in multiscale systems
• Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains
• Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in 2+1 dimensions
• Synchronization transition in space-time chaos in the presence of quenched disorder