Showing papers in "Physica D: Nonlinear Phenomena in 1985"

TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.

TL;DR: In this article, a simple system of ordinary differential equations is introduced which has applications to the dynamics of small molecules, molecular crystals, self-trapping in amorphous semiconductors, and globular proteins.

TL;DR: In this paper, the authors investigated fractal basin boundaries for dynamical systems and found that they can lead to great difficulty in predicting to which attractor a system eventually goes, and that fractal basins can be classified as being either locally connected or locally disconnected.

TL;DR: The Kuramoto-Sivashinsky equations model pattern formations on unstable flame fronts and thin hydrodynamic films and are characterized by the coexistence of coherent spatial structures with temporal chaos as mentioned in this paper.

TL;DR: This is the first, simple, biophysically realistic model for excitable cells that shows endogenous chaos, which consists of three first-order, non-linear differential equations, which represent ionic events in excitable membranes.

TL;DR: In this article, the average life time of a chaotic transient is related to the dimensions of the repeller, and to Lyapunov exponents of the flow on it.

TL;DR: In this paper, the stable steady states obtained by coupling two, three and more Brusselators in parallel, in a diffusion-like manner, are discussed, and the symmetry patterns of the stable domains are analyzed.

TL;DR: In this article, the problem of pattern selection in situations where a stable, nonuniform state of a nonlinear dissipative system propagates into an initially unstable, homogeneous region is discussed.

TL;DR: In this article, the stability of a two-dimensional plane-parallel flow of viscous liquid in an external force field which is a periodic function of one of the coordinates is investigated.

TL;DR: In this article, the boundaries of subharmonic and homoclinic bifurcations are calculated on the basis of the Melnikov method and of averaging methods for parametrically forced pendulum systems.

TL;DR: In this article, the frequency of quasiperiodic motions in non-conservative dynamical systems is studied numerically for flows on an N-torus for N = 3 and 4.

TL;DR: In this paper, a nonlinear equation for the evolution of slow modulations of the periodic pattern far from threshold but near the Eckhaus instability is derived and used to analyse the universal properties of the bifurcation.

TL;DR: An experimental study of periodic and chaotic type aperiodic motions of a parametrically harmonically excited pendulum is presented in this article, where it is shown that a characteristic route to chaos is the period-doubling cascade, which occurs with increasing driving amplitude and decreasing damping force.

TL;DR: In this article, an interesting three-dimensional generalization of the Henon map is announced, which yields a strange attractor for the parameter values a = 1.4, b = 0.3 has been investigated over the extended region -2≤ a ≤ 6, -1≤ b ≤ 1.

TL;DR: A model for homogeneous MHD turbulence is proposed in this paper, where nonlinear interactions act between nearest neighbours in a discretized wavenumbers space and conservation properties (total energy and v-b correlation) are verified.

TL;DR: In this article, it was shown that a 6-order system of nonlinear dynamo waves can be reduced to a fifth order system, with trajectories that lie on a 2-torus after the third bifurcation.

TL;DR: In this article, the authors developed a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics, which is consistent with the new interpretation that normal sinus rhythm may represent 1:1 coupling of two or more active oscillators and also accounts for the appearance of an AV block with critical changes in a single parameter such as the pacing rate.

TL;DR: In this paper, it was shown that the Iachello relation in nuclear physics may also be a manifestation of the BCS mechanism which is known to account for the nuclear pairing phenomenon.

TL;DR: In this article, the inelastic interactions of kinks and breathers in the sine-Gordon equation with different perturbations are considered, and in the presence of the dissipative perturbation the break-up of a breather into a kink-antikink pair due to the collision with a fast kink is investigated.

TL;DR: In this paper, a method for the numerical computation of invariant circles of maps is presented, along with appropriate techniques for its implementation, which involves solution of a functional equation by discretization and Newton iteration.

TL;DR: This work simulates excitability in a cubical three-dimensional grid of discrete cells and shows how topologically distinct organizing centers for self-sustaining rhythmic activity arise from suitable initial conditions.

TL;DR: In this article, the structure of the Mandelbrot set D and its boundary is investigated, where the set of points A ( s ) = {± 1 ± s ± s 2 ± s 3 ± … for all sequences of + and −}, generically a fractal.

TL;DR: In this article, the bifurcation structure in a two-parameter family of circle maps is considered and a generalization of the rotation number is given and symmetries of the Bifurcations in parameter space are described.

TL;DR: In this paper, the fractal dimension of the Poincare section of the two-well potential strange attractor has been calculated as a function of damping using a correlation function technique.

TL;DR: In this paper, a confusion over the concept of first integrals was clarified, and the clear distinction between first-integrals and functions which are first-independents only on a specific, fixed hypersurface was discussed.

TL;DR: Using a partial differential equation model of an excitable medium, the first computation of a topologically new vortex ring was presented in this article, which suggests distinctive properties whereby we may recognize this new organizing center in experiments with excitable media.

TL;DR: In this paper, the electrocardiographic record of a patient with the "sick sinus syndrome" demonstrated periodic behavior including subharmonic bifurcations in an attractor of the interbeat interval.

TL;DR: In this article, the authors derived the Hamiltonian structures of three theories: non-relativistic, special-relatiivistic and general-relateivistic adiabatic fluids, each in the Eulerian representation in Riemannian space (or Lorentzian spacetime).

TL;DR: In this paper, Modulational diffusion, a weak instability that frequently occurs in many-dimensional, nonlinear Hamiltonian systems, is studied both analytically and numerically.

TL;DR: Similarity transformations of the cubic Schrodinger equation (CSE) were used to remove the explicit time variation in the CSE and reduce it to differential equations in the spatial variables only as mentioned in this paper.