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

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

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

Nearest neighbor embedding with different time delays

A nearest neighbor based selection of time delays for phase space reconstruction is proposed and compared to the standard use of time delayed mutual information. The possibility of using different time delays for consecutive dimensions is considered. A case study of numerically generated solutions of the Lorenz system is used for illustration. The effect of contamination with various levels of additive Gaussian white noise is discussed.Comment: 4 pages, 5 figures, updated to final versio

Retrospective analysis of a nonforecasted rain-on-snow flood in the Alps – a matter of model limitations or unpredictable nature?

A rain-on-snow flood occurred in the Bernese Alps, Switzerland, on 10 October 2011, and caused significant damage. As the flood peak was unpredicted by the flood forecast system, questions were raised concerning the causes and the predictability of the event. Here, we aimed to reconstruct the anatomy of this rain-on-snow flood in the Lötschen Valley (160 km²) by analyzing meteorological data from the synoptic to the local scale and by reproducing the flood peak with the hydrological model WaSiM-ETH (Water Flow and Balance Simulation Model). This in order to gain process understanding and to evaluate the predictability. <br><br> The atmospheric drivers of this rain-on-snow flood were (i) sustained snowfall followed by (ii) the passage of an atmospheric river bringing warm and moist air towards the Alps. As a result, intensive rainfall (average of 100 mm day^-1) was accompanied by a temperature increase that shifted the 0° line from 1500 to 3200 m a.s.l. (meters above sea level) in 24 h with a maximum increase of 9 K in 9 h. The south-facing slope of the valley received significantly more precipitation than the north-facing slope, leading to flooding only in tributaries along the south-facing slope. We hypothesized that the reason for this very local rainfall distribution was a cavity circulation combined with a seeder-feeder-cloud system enhancing local rainfall and snowmelt along the south-facing slope. <br><br> By applying and considerably recalibrating the standard hydrological model setup, we proved that both latent and sensible heat fluxes were needed to reconstruct the snow cover dynamic, and that locally high-precipitation sums (160 mm in 12 h) were required to produce the estimated flood peak. However, to reproduce the rapid runoff responses during the event, we conceptually represent likely lateral flow dynamics within the snow cover causing the model to react "oversensitively" to meltwater. <br><br> Driving the optimized model with COSMO (Consortium for Small-scale Modeling)-2 forecast data, we still failed to simulate the flood because COSMO-2 forecast data underestimated both the local precipitation peak and the temperature increase. Thus we conclude that this rain-on-snow flood was, in general, predictable, but requires a special hydrological model setup and extensive and locally precise meteorological input data. Although, this data quality may not be achieved with forecast data, an additional model with a specific rain-on-snow configuration can provide useful information when rain-on-snow events are likely to occur

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