Universal occurrence of the phase-flip bifurcation in time-delay coupled systems
Recently, the phase-flip bifurcation has been described as a fundamental transition in time-delay coupled, phase-synchronized nonlinear dynamical systems. The bifurcation is characterized by a change ...
Recently, the phase-flip bifurcation has been described as a fundamental transition in time-delay coupled, phase-synchronized nonlinear dynamical systems. The bifurcation is characterized by a change ...
Chaotic scattering in solitary wave interactions: A singular iterated-map description
We derive a family of singular iterated maps—closely related to Poincaré maps—that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solit...
We derive a family of singular iterated maps—closely related to Poincaré maps—that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solit...
Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system
Chaos 18, 023112 (2008); doi:10.1063/1.2909862
Published 7 May 2008
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We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method.
©2008 American Institute of Physics
| History: | Received 13 November 2007; accepted 26 March 2008; published 7 May 2008 |
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