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

Anticipating the dynamics of chaotic maps

We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output reinjected after a certain delay. For a class of simple maps, we give analytic conditions for the stability of the synchronized solution, and present results of numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that agree well with the analytic predictions.Comment: Uses the elsart.cls (v2000) style (included). 9 pages, including 4 figures. New version contains minor modifications to text and 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

Anticipated synchronization in coupled chaotic maps with delays

We study the synchronization of two chaotic maps with unidirectional (master-slave) coupling. Both maps have an intrinsic delay $n_1$, and coupling acts with a delay $n_2$. Depending on the sign of the difference $n_1-n_2$, the slave map can synchronize to a future or a past state of the master system. The stability properties of the synchronized state are studied analytically, and we find that they are independent of the coupling delay $n_2$. These results are compared with numerical simulations of a delayed map that arises from discretization of the Ikeda delay-differential equation. We show that the critical value of the coupling strength above which synchronization is stable becomes independent of the delay $n_1$ for large delays.Comment: 10 pages, 4 figure

Characterization of the anticipated synchronization regime in the coupled FitzHugh--Nagumo model for neurons

We characterize numerically the regime of anticipated synchronization in the coupled FitzHugh-Nagumo model for neurons. We consider two neurons, coupled unidirectionally (in a master-slave configuration), subject to the same random external forcing and with a recurrent inhibitory delayed connection in the slave neuron. We show that the scheme leads to anticipated synchronization, a regime in which the slave neuron fires the same train of pulses as the master neuron, but earlier in time. We characterize the synchronization in the parameter space (coupling strength, anticipation time) and introduce several quantities to measure the degree of synchronization.Comment: 8 pages. Proceedings of the conference on "Stochastic Systems: From Randomness to"Complexit