Amplitude death in coupled chaotic oscillators

Amplitude death can occur in chaotic dynamical systems with time-delay coupling, similar to the case of coupled limit cycles. The coupling leads to stabilization of fixed points of the subsystems. This phenomenon is quite general, and occurs for identical as well as nonidentical coupled chaotic systems. Using the Lorenz and R\"ossler chaotic oscillators to construct representative systems, various possible transitions from chaotic dynamics to fixed points are discussed.Comment: To be published in PR

Local prediction of turning points of oscillating time series

For oscillating time series, the prediction is often focused on the turning points. In order to predict the turning point magnitudes and times it is proposed to form the state space reconstruction only from the turning points and modify the local (nearest neighbor) model accordingly. The model on turning points gives optimal prediction at a lower dimensional state space than the optimal local model applied directly on the oscillating time series and is thus computationally more efficient. Monte Carlo simulations on different oscillating nonlinear systems showed that it gives better predictions of turning points and this is confirmed also for the time series of annual sunspots and total stress in a plastic deformation experiment.Comment: 7 pages, 5 figures, 2 tables, submitted to PR

Peeling Bifurcations of Toroidal Chaotic Attractors

Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review

Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators

We propose a basic mechanism for isochronal synchrony and communication with mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators (IROs), mutually coupled with a propagation delay, synchronize isochronally when both are symmetrically driven by a third Ikeda oscillator. This synchronous operation, unstable in the two delay-coupled oscillators alone, facilitates simultaneous, bidirectional communication of messages with chaotic carrier waveforms. This approach to combine both bidirectional and unidirectional coupling represents an application of generalized synchronization using a mediating drive signal for a spatially distributed and internally synchronized multi-component system

Network synchronization of groups

In this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups. Both continuous time and discrete time systems are considered. We initially focus on the case where two groups are present and the network has bipartite topology (i.e., links exist between nodes in different groups but not between nodes in the same group). We also show that group synchronous motions are compatible with more general network topologies, where there are also connections within the groups

Spatial patterns of desynchronization bursts in networks

We adapt a previous model and analysis method (the {\it master stability function}), extensively used for studying the stability of the synchronous state of networks of identical chaotic oscillators, to the case of oscillators that are similar but not exactly identical. We find that bubbling induced desynchronization bursts occur for some parameter values. These bursts have spatial patterns, which can be predicted from the network connectivity matrix and the unstable periodic orbits embedded in the attractor. We test the analysis of bursts by comparison with numerical experiments. In the case that no bursting occurs, we discuss the deviations from the exactly synchronous state caused by the mismatch between oscillators

A Tool to Recover Scalar Time-Delay Systems from Experimental Time Series

We propose a method that is able to analyze chaotic time series, gained from exp erimental data. The method allows to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form $dy(t)/dt = h(y(t),y(t-\tau_0))$, the delay time $\tau_0$ and the functi on $h$ can be recovered. There are no restrictions to the dimensionality of the chaotic attractor. The method turns out to be insensitive to noise. We successfully apply the method to various time series taken from a computer experiment and two different electronic oscillators

Spin-orbit coupling and intrinsic spin mixing in quantum dots

Spin-orbit coupling effects are studied in quantum dots in InSb, a narrow-gap material. Competition between different Rashba and Dresselhaus terms is shown to produce wholesale changes in the spectrum. The large (and negative) $g$-factor and the Rashba field produce states where spin is no longer a good quantum number and intrinsic flips occur at moderate magnetic fields. For dots with two electrons, a singlet-triplet mixing occurs in the ground state, with observable signatures in intraband FIR absorption, and possible importance in quantum computation.Comment: REVTEX4 text with 3 figures (high resolution figs available by request). Submitted to PR

Chaos and Synchronized Chaos in an Earthquake Model

We show that chaos is present in the symmetric two-block Burridge-Knopoff model for earthquakes. This is in contrast with previous numerical studies, but in agreement with experimental results. In this system, we have found a rich dynamical behavior with an unusual route to chaos. In the three-block system, we see the appearance of synchronized chaos, showing that this concept can have potential applications in the field of seismology.Comment: To appear in Physical Review Letters (13 pages, 6 figures