Showing papers in "Physica D: Nonlinear Phenomena in 2007"

TL;DR: A practical method for data assimilation in large, spatiotemporally chaotic systems, a type of “ensemble Kalman filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states.

TL;DR: In this article, the authors review linkages to optimal interpolation, kriging, Kalman filtering, smoothing, and variational analysis for data assimilation in Bayesian statistics.

TL;DR: Results of ongoing calculations covering the period of the World Ocean Circulation Experiment, and including among other data, satellite altimetry from TOPEX/POSEIDON, Jason-1, ERS- 1/2, ENVISAT, and GFO, a global array of profiling floats from the Argo program, and satellite gravity data from the GRACE mission, suggest that the solutions are now useful for scientific purposes.

TL;DR: In this article, the authors study a class of swarming problems where particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism and find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters.

TL;DR: In this paper, a hierarchical ensemble filter is proposed to estimate the impact of an observation to state variables that are "close" to the observation, where an ensemble of ensemble filters is used to detect sampling error.

TL;DR: The generalised Kuramoto model is generalised to allow one to model neuronal synchronisation more appropriately and allow for the adaptive nature of neurons in the brain to be accommodated.

TL;DR: The generalized alignment index of order k (GALIk) as mentioned in this paper is a generalization of the Smaller Alignment Index (SALI) that allows to distinguish between chaotic behavior and quasiperiodic motion on N-dimensional tori.

TL;DR: In this article, the authors compare different synchronization measures with respect to their ability to distinguish between different levels of coupling and their robustness against noise and show that the measure to be applied to a certain task can not be chosen according to a fixed criterion but rather pragmatically as the measure which most reliably yields plausible information in test applications, although certain dynamical features of a system under investigation may render certain measures more suitable than others.

TL;DR: In this paper, the authors studied the dynamics of a virus infection model under the assumption that the immune response is retarded and showed that if the basic reproductive ratio of the virus is less than one, the infection-free equilibrium is globally asymptotically stable.

TL;DR: Results indicate that error estimates, ensemble sizes, error subspace ranks, covariance tapering parameters and stochastic error models can be calibrated by such quantitative adaptation.

TL;DR: In this article, a range of techniques for probing the posterior distribution, based around the Langevin equation, are proposed and compared with existing methods, and the relationship between the Bayesian approach outlined here and the commonly used Kalman filter based techniques, prevalent in practice, is discussed.

TL;DR: In this paper, a passive controller is designed and synchronization of two identical unified chaotic systems with different initial conditions is realized using passive control and simulation results for two Lorenz, two Lu and two Chen chaotic systems are provided to show the effectiveness of the proposed synchronization method.

TL;DR: In this article, a continuation approach to the computation of essential and absolute spectra of dierential operators on the real line is presented, compared with direct eigenvalue computations for the discretized operator, are the ecient and accurate computation of selected parts of the spectrum (typically those near the imaginary axis) and the option to compute nonlinear travelling waves and selected eigenvalues or other stability indicators simultaneously.

TL;DR: In this article, the authors provide a generic set of necessary and sufficient conditions for the ensemble Kalman filter to be centred on the analysis state estimate (unbiased), and provide simple proofs and examples, as well as a mathematical description of the set of unbiased ensemble SRFs.

TL;DR: In this article, a decomposition of matrix model partition functions is proposed, which is the matrix model version of multi-instanton and multi-meron configurations in Yang-Mills theories.

TL;DR: In this paper, the existence of 2 n stable stationary solutions for a general n-dimensional delayed neural networks with several classes of activation functions was established through formulating parameter conditions motivated by a geometrical observation.

TL;DR: In this paper, a survey of particle filters for nonlinear filtering is presented, with a special emphasis on an important family of schemes known as the particle filters, and a numerical study is presented to illustrate that in settings where the signal/observation dynamics are non linear a suitably chosen nonlinear scheme can drastically outperform the extended Kalman filter.

TL;DR: In this article, it was shown that the class of nested canalyzing functions is equal to that of unate cascade functions, and that their analysis is an algebraic variety which makes their analysis amenable to the use of algebraic geometry and computational algebra.

TL;DR: In this article, the authors present a discussion that exhibits the superiority of the Bandt-Pompe approach to the extraction of a probability distribution from time series values, which is related to our work.

TL;DR: This paper proposes a method that accounts for both position and amplitude errors in data assimilation, and demonstrates with 1D and 2D examples how applying field alignment produces better analyses with sparse and uncertain observations.

TL;DR: In this paper, a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability is presented, where the appropriate amplitude equations are the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1).

TL;DR: In this article, the authors investigated the Bogdanov-Takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method, and predicted the suitable choice in the feedback control in order to obtain the asymptotic stable state.

TL;DR: A sufficient synchronization criterion for a general linear state error feedback controller is rigorously proven by means of linearization and Lyapunov’s direct methods and the optimized criteria are applied to four typical generalized Lorenz systems, obtaining precise corresponding synchronization conditions.

TL;DR: In this paper, the authors proposed several examples of smooth low-order autonomous dynamical systems which have uniformly hyperbolic attractors, where, due to certain amplitude nonlinearities, successive epochs of damped and excited oscillations alternate.

TL;DR: Cessac and Sepulchre as discussed by the authors considered a class of two-dimensional time-discrete maps describing simple rotator models with a contracting radial dynamics onto the unit circle and a chaotic angular dynamics.

TL;DR: In this paper, the authors analyzed the phase space of a reversible dynamical system describing the stationary solutions of a model for a nonlinear optical cavity and found that the stable and unstable manifolds of homogeneous and patterned solutions present a much higher level of complexity than predicted, including the existence of additional localized solutions and fronts.

TL;DR: In this article, Milstein and Tretyakov proposed a quasi-symplectic integrator for Langevin-type equations with nonglobally Lipschitz coefficients.

TL;DR: In this paper, a recursive back-stepping nonlinear control technique is employed to control intermittent chaos and then track a desired trajectory by means of the same technique. But the authors consider the problem of controlling chaotic motion and deterministic directed transport in inertia ratchets.

TL;DR: In this paper, a three-parametric phase diagram of the classical Lorenz model has been analyzed by combining the combined use of the OFLI2 Chaos Indicator and the classical Maximum Lyapunov Exponent, which have permitted a fast and complete location of the chaotic parameter region.

TL;DR: A new measure for information propagation based on perturbation avalanches in Boolean networks is proposed and it is found that the measure is maximized in dynamically critical networks and in subcritical networks if noise is present.