Showing papers in "Physica D: Nonlinear Phenomena in 2002"

TL;DR: This work proposes a novel measure for generalized synchronization in multivariate data sets which avoids this bias and can deal with non-stationary dynamics.

TL;DR: Only in the case of zero transfer entropy in one direction the authors can reliably infer an asymmetry of the information exchange, and it is shown that finite length scale estimates converge from below and can be used to reject the assumption that the observed processes are independent.

TL;DR: In this article, the orthogonal dynamics equation is used to evaluate a non-Markovian memory term, where the initial conditions for the unresolved components of the solution are drawn from a probability distribution, and their effect on a small set of variables that are actually computed is evaluated via statistical projection.

TL;DR: In this paper, the analysis of sliding bifurcations in n-dimensional piecewise-smooth dynamical systems with discontinuous vector fields is studied. And the derivation of appropriate normal-form maps is detailed.

TL;DR: In this article, the authors estimate the errors due to observational noise on the recurrence quantification analysis (RQA) based on this estimation, and present ways to minimize these errors.

TL;DR: In this article, the existence and stability of linear invariant manifolds in a network of coupled identical dynamical systems is studied, where symmetry under permutation of different units of the network is helpful to construct explicit formulae for linear invariants.

TL;DR: In this article, the authors studied non-trivial firing patterns in small assemblies of pulse-coupled oscillatory maps and found conditions for the existence of waves in rings of coupled maps that are coupled bi-directionally.

TL;DR: The motion of plane curves in Klein geometry is studied in this paper, where it is shown that the KdV, Harry-Dym, Sawada-Kotera, Burgers, the defocusing mKdV hierarchies, the Camassa-Holm and the Kaup-Kupershmidt equation naturally arise from the motions of planes in SL(2)-, Sim(2), SA(2) and A(2-) geometries.

TL;DR: In this paper, sufficient conditions for the globally asymptotic stability of a unique equilibrium for the Cohen-Grossberg neural network with multiple delays were established without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections.

TL;DR: In this paper, the authors compared the asymptotic expansions of the intrinsic low-dimensional manifold (ILDM) and the slow manifold given by geometric singular perturbation theory.

TL;DR: In this article, a robust shooting algorithm based on exterior algebra spaces is introduced to solve the spectral problem associated with the linearization about solitary waves of the generalized fifth-order KdV equation.

TL;DR: In this article, the static and dynamic behavior of well localized solitary solutions of a three-component reaction-diffusion model in two-and three-dimensional space is investigated, where the field equations are reduced to a set of ordinary differential equations describing rather well the dynamical behaviour of isolated and interacting dissipative solitons using their center coordinates and amplitudes of certain propagator modes.

TL;DR: In this article, the authors compare two tools for detecting the geometry of resonances of a dynamical system in order to get information about the long-term stability of chaotic solutions.

TL;DR: In this article, the authors investigated the bifurcation patterns of the two-strain SIR model with seasonal forcing in transmission rate, and they found that the period doubling bifurbation occurs as the strength of seasonal forcing is increased.

TL;DR: In this article, a priori tests of a systematic stochastic mode reduction procedure for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables are developed.

TL;DR: In this article, the authors numerically investigate nonlinear Schrodinger equations with a stochastic contribution which is of white noise type and acts either as a potential (multiplicative noise) or as a forcing term (additive noise).

TL;DR: In this article, it was shown that if there are travelling pulses which primarily and super-critically bifurcate from a standing pulse when some parameter is varied, they possess reflection mechanism if the velocity is very slow.

TL;DR: In this article, the authors describe some numerical experiments giving evidence of Wada basin boundaries for the Duffing oscillator and suggest mechanisms by which this fractal property of the boundaries appears and discuss the difficulties that the Wada property presents for predicting the behavior of dynamical systems.

TL;DR: RBNs are used to examine regulatory gene networks with four different topologies, which are characterized by different rank distributions of output connections that vary from uniform to highly skewed and also examine effects of bias in the distribution of Boolean functions for the network.

TL;DR: In this article, the authors considered the problem of giant wave formation on water of finite depth and suggested dispersive focusing in a nonlinear medium as a possible mechanism for giant wave generation.

TL;DR: This paper discusses existing techniques that attempt to address this hypothesis and introduces a new approach that generates surrogates that are constrained and for cyclic time series tests the null hypothesis of a periodic orbit with uncorrelated noise.

TL;DR: In this article, the existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators are considered.

TL;DR: In this paper, the authors follow a two-stage testing procedure to test for nonlinearities and chaos in real exchange rates, using a new set of techniques designed by Webber and Zbilut, called recurrence quantification analysis (RQA).

TL;DR: In this paper, a model derived by Fei et al. of a kink solution to the sine-Gordon equation interacting with an impurity mode is investigated using the tools of dynamical systems, and it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect.

TL;DR: In this article, the authors investigate one-parameter families of two-dimensional bright spinning solitons (ring vortices) in dispersive media combining cubic self-focusing and quintic self-defocusing nonlinearities.

TL;DR: In this article, a 4-vector ζ is constructed out of a combination of scalar and vector products of the vorticity ω and the vortex stretching vector ω ·∇ u = Sω.

TL;DR: Combining the small-amplitude approximation with THC yields in new gm turbulence closure equations for compressible fluids in the EP variational framework, based on the linearized fluctuation relations between Eulerian and Lagrangian fluctuations.

TL;DR: In this paper, a nonlinear controller called the backstepping controller is applied to suppress the chaotic motion of a modified Chua's circuit system, which achieves global exponential stability in the sense that the attraction basin for the reference state is the entire state space.

TL;DR: In this paper, the continuous spectrum and soliton solutions for the Boussinesq equation are investigated using the ∂-dressing method, and a systematic study of the solitonic sector is presented.

TL;DR: In this article, a new method for parameter estimation in systems with nonlinear spatio-temporal dynamics is described, which is able to reliably determine parameter estimates from noisy data and is even applicable in cases with unobserved components.