ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS

Abstract

A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is derived on the basis of this relationship. An approximate expression for the nonlinear velocity is also determined by extending the concept of Lyapunov exponent to growth rate of finite perturbations.

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References in corpus (3)

• Structural Stability and Renormalization Group for Propagating Fronts
• On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation
• Linear And Nonlinear Mechanisms Of Information Propagation

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• Transition to Stochastic Synchronization in Spatially Extended Systems
• Breakdown of the standard Perturbation Theory and Moving Boundary Approximation for "Pulled" Fronts
• Linear and nonlinear information flow in spatially extended systems
• Dynamical properties of the synchronization transition
• Chronotopic Lyapunov Analysis: (II) towards a Unified Approach
• Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
• Stable chaos in fluctuation driven neural circuits
• On finite-size Lyapunov exponents in multiscale systems
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in 2+1 dimensions
• Many universality classes in an interface model restricted to non-negative heights
• Synchronization and partial synchronization of linear maps
• Role of chaos for the validity of statistical mechanics laws: diffusion and conduction