Fractalization of Torus Revisited as a Strange Nonchaotic Attractor

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency.Comment: Latex file ( figures will be sent electronically upon request):submitted to Phys.Rev. E (1996

Condensation in Globally Coupled Populations of Chaotic Dynamical Systems

The condensation transition, leading to complete mutual synchronization in large populations of globally coupled chaotic Roessler oscillators, is investigated. Statistical properties of this transition and the cluster structure of partially condensed states are analyzed.Comment: 11 pages, 4 figures, revte

On the validity of ADM formulation in 2D quantum gravity

We investigate 2d gravity quantized in the ADM formulation, where only the loop length $l(z)$ is retained as a dynamical variable of the gravitation, in order to get an intuitive physical insight of the theory. The effective action of $l(z)$ is calculated by adding scalar fields of conformal coupling, and the problems of the critical dimension and the time development of $l$ are addressed.Comment: 12 page

Clustering data by inhomogeneous chaotic map lattices

A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system corresponds to a macroscopic attractor independent of the initial conditions. The mutual information between couples of maps serves to partition the data set in clusters, without prior assumptions about the structure of the underlying distribution of the data. Experiments on simulated and real data sets show the effectiveness of the proposed algorithm.Comment: 8 pages, 6 figures. Revised version accepted for publication on Physical Review Letter

Two-parameter neutrino mass matrices with two texture zeros

We reanalyse Majorana-neutrino mass matrices M_nu with two texture zeros, by searching for viable hybrid textures in which the non-zero matrix elements of M_nu have simple ratios. Referring to the classification scheme of Frampton, Glashow and Marfatia, we find that the mass matrix denoted by A1 allows the ratios (M_nu)_{mu mu} : (Mnu)_{tau tau} = 1:1 and (M_nu)_{e tau} : (Mnu)_{mu tau} = 1:2. There are analogous ratios for texture A2. With these two hybrid textures, one obtains, for instance, good agreement with the data if one computes the three mixing angles in terms of the experimentally determined mass-squared differences Delta m^2_21 and Delta m^2_31. We could not find viable hybrid textures based on mass matrices different from those of cases A1 and A2.Comment: 10 pages, no figures, minor changes, some references adde

Coupling Of The B1g Phonon To The Anti-Nodal Electronic States of Bi2Sr2Ca0.92Y0.08Cu2O(8+delta)

Angle-resolved photoemission spectroscopy (ARPES) on optimally doped Bi2Sr2Ca0.92Y0.08Cu2O(8+delta) uncovers a coupling of the electronic bands to a 40 meV mode in an extended k-space region away from the nodal direction, leading to a new interpretation of the strong renormalization of the electronic structure seen in Bi2212. Phenomenological agreements with neutron and Raman experiments suggest that this mode is the B1g oxygen bond-buckling phonon. A theoretical calculation based on this assignment reproduces the electronic renormalization seen in the data.Comment: 4 Pages, 4 Figures Updated Figures and Tex

Phase transition and correlation decay in Coupled Map Lattices

For a Coupled Map Lattice with a specific strong coupling emulating Stavskaya's probabilistic cellular automata, we prove the existence of a phase transition using a Peierls argument, and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling. This implies the exponential decay, in space and in time, of the correlation functions of the invariant measures

Proportion Regulation in Globally Coupled Nonlinear Systems

As a model of proportion regulation in differentiation process of biological system, globally coupled activator-inhibitor systems are studied. Formation and destabilization of one and two cluster state are predicted analytically. Numerical simulations show that the proportion of units of clusters is chosen within a finite range and it is selected depend on the initial condition.Comment: 11 pages (revtex format) and 5 figures (PostScript)

Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators

Peter Ashwin and Jon Borresen, Physical Review E, Vol. 70, p. 026203 (2004). "Copyright © 2004 by the American Physical Society."We study properties of the dynamics underlying slow cluster oscillations in two systems of five globally coupled oscillators. These slow oscillations are due to the appearance of structurally stable heteroclinic connections between cluster states in the noise-free dynamics. In the presence of low levels of noise they give rise to long periods of residence near cluster states interspersed with sudden transitions between them. Moreover, these transitions may occur between cluster states of the same symmetry, or between cluster states with conjugate symmetries given by some rearrangement of the oscillators. We consider the system of coupled phase oscillators studied by Hansel et al. [Phys. Rev. E 48, 3470 (1993)] in which one can observe slow, noise-driven oscillations that occur between two families of two cluster periodic states; in the noise-free case there is a robust attracting heteroclinic cycle connecting these families. The two families consist of symmetric images of two inequivalent periodic orbits that have the same symmetry. For N=5 oscillators, one of the periodic orbits has one unstable direction and the other has two unstable directions. Examining the behavior on the unstable manifold for the two unstable directions, we observe that the dimensionality of the manifold can give rise to switching between conjugate symmetry orbits. By applying small perturbations to the system we can easily steer it between a number of different marginally stable attractors. Finally, we show that similar behavior occurs in a system of phase-energy oscillators that are a natural extension of the phase model to two dimensional oscillators. We suggest that switching between conjugate symmetries is a very efficient method of encoding information into a globally coupled system of oscillators and may therefore be a good and simple model for the neural encoding of information