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Showing papers in "Physica D: Nonlinear Phenomena in 1997"


Journal ArticleDOI
TL;DR: A practical method to determine the minimum embedding dimension from a scalar time series that has the following advantages: does not contain any subjective parameters except for the time-delay for the embedding.

1,485 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that there exist spatially localized and time periodic solutions (breathers) in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong.

620 citations


Journal ArticleDOI
TL;DR: In this article, the authors extend the notion of phase locking to the case of chaotic oscillators and investigate the phase dynamics of a single self-sustanined chaotic oscillator subjected to external force.

518 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a procedure to construct time-stepping algorithms that approximate the flow of continuous ODEs for mechanical systems by discretizing Hamilton's principle rather than the equations of motion.

324 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that recurrence plots (RPs) give detailed characterizations of time series generated by dynamical systems driven by slowly varying external forces, and the same results hold for stochastic systems if the RP of the time series is suitably averaged and transformed.

243 citations


Journal ArticleDOI
TL;DR: In this paper, a semi-quantitative nonlinear field theory of the brain under realistic anatomical connectivity conditions describing the interaction between functional units within the brain is presented, which is derived from the quasi-microscopic conversion properties of neural populations occurring at synapses and somas.

219 citations


Journal ArticleDOI
TL;DR: In this paper, a delay-differential equation was used to model an artificial neural network with two neurons and a linear stability analysis provided parameter values yielding asymptotic stability of the stationary solutions.

216 citations


Journal ArticleDOI
TL;DR: In this article, an efficient and numerically stable method to determine all the Lyapunov characteristic exponents of a dynamical system is developed, highlighting some aspects of convergence, accuracy and efficiency.

207 citations


Journal ArticleDOI
TL;DR: In this article, an impulsive control scheme of the Lorenz system is presented, where the theory of impulsive differential equation is used to find conditions under which impulsively controlled system is asymptotically stable.

180 citations


Journal ArticleDOI
TL;DR: In this article, the effects of inertial terms on the stability of the fixed points of a Hopfield (1984) effective-neuron system were explored and the chaos was confirmed by Lyapunov exponents, power spectra, and phase space plots.

168 citations


Journal ArticleDOI
TL;DR: In this article, the authors illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of elementary one-dimensional cellular automaton rule 54.

Journal ArticleDOI
TL;DR: It is shown that this unique fixed point in TCNN can actually evolve into a snap-back repeller which generates chaotic structure, if several conditions are satisfied, and the obtained theoretical results hold for a wide class of discrete-time neural networks.

Journal ArticleDOI
TL;DR: The simulation results of this paper indicate that recurrent networks filter noise more successfully than feedforward networks in small as well as large samples.

Journal ArticleDOI
TL;DR: In this article, the stability theory of relative equilibria for mechanical systems with symmetry was developed and applied to underwater vehicle dynamics, and conditions for Liapunov stability of the steadily rising and possibly spinning, bottom-heavy vehicle, which corresponds to a relative equilibrium with nongeneric momentum.

Journal ArticleDOI
TL;DR: In this article, a large system of nonlinear phase oscillators with sinusoidal nonlinearity, uniformly distributed natural frequencies and global all-to-all coupling is analyzed.

Journal ArticleDOI
TL;DR: Results show that cooperation between elements using a simple interaction strongly enhances the performance of the group compared to independent individuals.

Journal ArticleDOI
TL;DR: In this paper, the authors study the linear stability of the full, time-independent, equations by introducing a new are length preserving perturbation scheme, which gives a direct proof of the existence of dynamical instabilities and provides the selection mechanism for the shape of unstable filaments.

Journal ArticleDOI
TL;DR: The main results of the studies of information transmission in the human cerebral cortex are given, based on the mutual information theory of Vastano and Swinney (1988), and the transmission intensities were characterized by complexity measures.

Journal ArticleDOI
TL;DR: In this article, the authors present a compact linear mode representation of the Hamiltonian of the FPU system with quartic nonlinearity and periodic boundary conditions, with explicitly computed mode coupling coefficients.

Journal ArticleDOI
TL;DR: In this paper, a simple genetic algorithm consisting of selection, mutation and crossover is used to search for the ground states of simple random Ising-spin systems: a random-field ideal paramagnet and a spin-glass chain.

Journal ArticleDOI
TL;DR: In this article, the authors investigate a different mechanism that can lead to nonhyperbolicity in typical invertible (respectively noninvertible) maps of dimension 3 and higher.

Journal ArticleDOI
TL;DR: In this article, the authors consider the case where for a fixed input the driven system is contracting; this is for instance the situation in certain classes of filters, and in the study of synchronization.

Journal ArticleDOI
TL;DR: In this paper, numerical solutions to the barotropic, β-plane, potential vorticity equation with viscosity are used to study Lagrangian transport in numerically generated, time-dependent, two-dimensional (2D) vector fields.

Journal ArticleDOI
TL;DR: In this article, the existence of self-sustained saturated solutions of the real Ginzburg-Landau equation subject to a boundary condition at x = 0 is rigorously determined and the scaling behavior of the NG modes close to threshold is derived.

Journal ArticleDOI
TL;DR: In this article, the chaotic hypothesis discussed in Gallavotti and Cohen (1995) is tested experimentally in a simple conduction model and the results suggest the validity of the hypothesis in the much wider context in which, as the forcing strength grows, the attractor ceases to be an Anosov system and becomes an Axiom A attractor.

Journal ArticleDOI
TL;DR: In this article, a short review on systems which exhibit non-self-averaging effects: sums of random variables when the distribution has a long tail, mean field spin glasses, random map models and returns of a random walk to the origin.

Journal ArticleDOI
TL;DR: In this article, the solitary waves in coupled nonlinear Schrodinger equations are classified into infinite families and the parameter regions of these solution families are novel and irregular, while the parameter dependence of the solitary wave is sensitive.

Journal ArticleDOI
TL;DR: In this paper, the Dirichlet boundary conditions were considered for coupled nonlinear oscillators with external periodic forces and it was shown that synchronization occurs provided that the coupling is dissipative and the coupling coefficients are sufficiently large.

Journal ArticleDOI
TL;DR: In this paper, the joint probability distribution p(ν1, L1; ν2, L2) for two velocity increments ν 1, ν 2 of different length scales L 1, L 2 was evaluated.

Journal ArticleDOI
TL;DR: A new model of CAs ( fuzzy CA s) is defined which allows the observation of interesting “chaotic” properties of elementary CAs and a measure which gives information about the CA's dynamics solely on the basis of the rule table and provides theoretical explanations to some of the empirical observations.