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Showing papers in "Physica D: Nonlinear Phenomena in 1992"


Journal ArticleDOI
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.

15,225 citations


Journal ArticleDOI
TL;DR: In this article, a statistical approach for identifying nonlinearity in time series is described, which first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate sets.

3,405 citations


Journal ArticleDOI
TL;DR: Singular spectrum analysis (SSA) is used in this article to estimate the lagged-covariance matrix of the processes studied, which is the basis of SSA.

1,334 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the correlation dimension of the Grassberger-Procaccia algorithm cannot exceed the value 2 log 10N if N is the number of points in the time series, and when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present.

631 citations


Journal ArticleDOI
TL;DR: In this paper, the existence and multiplicity of coherent structures in the complex Ginzburg-Landau equation was studied. But the authors focused on the competition between fronts and pulses and did not consider the non-uniformly translating front structures.

482 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter μ, and they show that stable periodic orbits occur frequently in such situations, but never or almost never occur in smooth systems.

457 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter.

401 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the nonlinear Schrodinger (NLS) equation is a combination of weak turbulence theory and condensate and collapse formation, and that the number of particles lost in an individual collapse event is virtually independent of damping.

398 citations


Journal ArticleDOI
TL;DR: A global ocean model on the massively parallel CM-2 Connection Machine based on the Bryan-Cox-Semtner ocean general circulation model is developed, with major changes that were made in the algorithms and numerical methods.

389 citations


Journal ArticleDOI
TL;DR: In this paper, Laskar's analysis of the fundamental frequencies of a hamiltonian system was applied to the standard mapping of the solar system and the results showed that the golden curve does not survive for a = 0.9718 which is very close and compatible with Greene's value ac = 0971635.

335 citations


Journal ArticleDOI
TL;DR: In this article, the success of current attempts to distinguish between low-dimensional chaos and random behavior in a time series of observations is considered, and several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory.

Journal ArticleDOI
TL;DR: The algorithm estimates not only the largest but all Lyapunov exponents of the unknown system by a multivariate feedforward network estimation technique and is very satisfactory in the presence of noise as well as with limited number of observations.

Journal ArticleDOI
TL;DR: In this paper, a closed-form solution to principal component analysis in the limit of small window widths is derived, which explains the relationship between delays, derivatives, and principal components, and shows how the singular spectrum scales with dimension and delay time.

Journal ArticleDOI
TL;DR: In this article, a topological procedure for analyzing chaotic time series is developed, which identifies the stretching and squeezing mechanisms responsible for chaotic behavior in low-dimensional dynamical systems, quantitatively described by a "template" or "knot-holder" can then be used to model the processes which generate the original chaotic data set.

Journal Article
TL;DR: In this paper, the conformal weights of L-state restricted solid-on-solid lattice models and their fusion hierarchies are calculated analytically in terms of Rogers dilogarithm.

Journal ArticleDOI
TL;DR: In this article, the authors developed new global perturbation techniques for detecting homoclinic trajectories in a class of four dimensional ordinary differential equations that are perturbations of completely integrable two-degree-of-freedom Hamiltonian systems.

Journal ArticleDOI
TL;DR: In this paper, the effects of symmetry breaking O(2) to D4 on an interaction between Fourier modes with wavenumbers in the ratio 1 : 2 were studied. And the effect of introducing riblets on a wall to reduce boundary layer drag was discussed.

Journal ArticleDOI
TL;DR: In this article, the Cauchy problem for the derivative nonlinear Schrodinger equation was studied in the weighted Sobolev space and in the Schwartz class, and it was shown that there is a unique global existence of solutions to this problem.

Journal ArticleDOI
TL;DR: In this article, a finite difference approximation of the full Navier-Stokes equations and explicit tracking of the interface between the fluids is used to simulate three-dimensional flows of two or more immiscible fluids separated by a sharp interface with finite surface tension.

Journal ArticleDOI
TL;DR: In this article, a global nonlinear predictor is introduced which attempts to correct systematic bias due to the inhomogeneous distribution of data common in strange attractors, and the significance of these results is established by comparison with results from similar surrogate series, generated so as not to contain the property of interest.

Journal ArticleDOI
TL;DR: A numerical algorithm is presented for the purpose of reducing noise from a discretely sampled input signal where the underlying signal of interest has a broadband spectrum, based on time delay embedding using coordinates generated by local low-pass filtering.

Journal ArticleDOI
TL;DR: In this paper, the authors describe phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing, leading to the formation of spatial patterns such as stripes, hexagons and spatio-temporal intermittent states, reminiscent of chemical and magnetical systems.

Journal ArticleDOI
TL;DR: In this article, the authors consider the 2D Navier-Stokes equations on a square with periodic boundary conditions and show that if the asymptotic behavior of the average of solutions on these subsquares (finite volume elements) is known, then the large time behaviour of the solution itself is completely determined, provided N is large enough.

Journal ArticleDOI
TL;DR: In this paper, the Eckhaus instability for traveling waves is studied experimentally, theoretically and numerically, and the existence of stable compression pulses is established in a certain domain of parameters.

Journal ArticleDOI
TL;DR: Fluctuation of the mean field is studied for a network of chaotic elements with the use of globally coupled maps as the size of the chaotic elements increases as discussed by the authors, where the remaining variance is roughly proportional to 1Nc.

Journal ArticleDOI
TL;DR: A comparison of four methods, which simultaneously estimate the two embedding parameters (delay time τ and sufficiently large embedding dimension dimE) for Takens' delay time coordinates, and a simple algorithm, which observes the spreading of trajectories at the transition from dimE to dimE + 1 and gives the opportunity to estimate the correlation entropy K2.

Journal ArticleDOI
TL;DR: In this article, the reliability of singular-value decomposition for reconstructing the attractor from one-dimensional chaotic time series has been investigated and doubts about its reliability are confirmed: singular value decomposition can bring distorted and misleading results when nonlinear structures are studied.

Journal ArticleDOI
TL;DR: In this paper, an estimator of dimension is described that has many advantages over the conventional implementation of the Grassberger-Procaccia method and can in some circumstances provide a confidence interval for the dimension estimate.

Journal ArticleDOI
TL;DR: In this paper, a mathematical model of thermally activated phase separation in binary systems is proposed based on the Landau-Ginzburg theory of phase transitions and non-equilibrium thermodynamics.

Journal ArticleDOI
TL;DR: Stability of the symbiotic network is dynamically sustained through this weak high-dimensional chaos, termed “homeochaos”, which resolves the paradox of mutation rates; paradox on the stability of a rule to change itself.