Impact of lag information on network inference

Extracting useful information from data is a fundamental challenge across disciplines as diverse as climate, neuroscience, genetics, and ecology. In the era of ``big data'', data is ubiquitous, but appropriated methods are needed for gaining reliable information from the data. In this work we consider a complex system, composed by interacting units, and aim at inferring which elements influence each other, directly from the observed data. The only assumption about the structure of the system is that it can be modeled by a network composed by a set of $N$ units connected with $L$ un-weighted and un-directed links, however, the structure of the connections is not known. In this situation the inference of the underlying network is usually done by using interdependency measures, computed from the output signals of the units. We show, using experimental data recorded from randomly coupled electronic R{\"o}ssler chaotic oscillators, that the information of the lag times obtained from bivariate cross-correlation analysis can be useful to gain information about the real connectivity of the system

Persistence and Stochastic Periodicity in the Intensity Dynamics of a Fiber Laser During the Transition to Optical Turbulence

Many natural systems display transitions among different dynamical regimes, which are difficult to identify when the data is noisy and high dimensional. A technologically relevant example is a fiber laser, which can display complex dynamical behaviors that involve nonlinear interactions of millions of cavity modes. Here we study the laminar-turbulence transition that occurs when the laser pump power is increased. By applying various data analysis tools to empirical intensity time series we characterize their persistence and demonstrate that at the transition temporal correlations can be precisely represented by a surprisingly simple model.Comment: 10 pages, 13 figure

Random Delays and the Synchronization of Chaotic Maps

We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the synchronized state is a homogeneous steady-state, where the chaotic dynamics of the individual maps is suppressed. This differs drastically from the synchronization with instantaneous and fixed-delay coupling, as in those cases the dynamics is chaotic. Also in contrast with the instantaneous and fixed-delay cases, the synchronization does not dependent on the connection topology, depends only on the average number of links per node. We find a scaling law that relates the distance to synchronization with the randomness of the delays. We also carry out a statistical linear stability analysis that confirms the numerical results and provides a better understanding of the nontrivial roles of random delayed interactions.Comment: 5 pages, 5 figure

Inferring long memory processes in the climate network via ordinal pattern analysis

We use ordinal patterns and symbolic analysis to construct global climate networks and uncover long and short term memory processes. The data analyzed is the monthly averaged surface air temperature (SAT field) and the results suggest that the time variability of the SAT field is determined by patterns of oscillatory behavior that repeat from time to time, with a periodicity related to intraseasonal oscillations and to El Ni\~{n}o on seasonal-to-interannual time scales.Comment: 10 pages, 13 figures Enlarged version, new sections and figures. Accepted in Chao

Predictability of Extreme Intensity Pulses in Optically Injected Semiconductor Lasers

The predictability of extreme intensity pulses emitted by an optically injected semiconductor laser is studied numerically, by using a well-known rate equation model. We show that symbolic ordinal time-series analysis allows to identify the patterns of intensity oscillations that are likely to occur before an extreme pulse. The method also gives information about patterns which are unlikely to occur before an extreme pulse. The specific patterns identified capture the topology of the underlying chaotic attractor and depend on the model parameters. The methodology proposed here can be useful for analyzing data recorded from other complex systems that generate extreme fluctuations in their output signals

Coexistence of attractors in a laser diode with optical feedback from a large external cavity

The coexistence of several attractors in the coherent collapsed state of a laser diode with optical feedback is investigated. These attractors are unstable tori that bifurcate from different external cavity modes. As the feedback rate is increased, these tori undergo different types of quasiperiodic routes, such as frequency locking, period doubling, or the appearance of a third incommensurate frequency. In the fully developed coherent collapsed state, the tori are all unstable, and the phenomenon of intermittence appears. Lyapunov exponent calculations demonstrate that this state presents hyperchaotic and high-dimensional dynamics. These results are explained qualitatively in terms of the multiattractor behavior found.Peer ReviewedPostprint (published version