Revival of oscillation from mean-field-induced death : Theory and experiment

Submitted ACKNOWLEDGMENTS T. B. acknowledges the financial support from SERB, Department of Science and Technology (DST), India [Project Grant No.: SB/FTP/PS-005/2013]. D. G. acknowledges DST, India, for providing support through the INSPIRE fellowship. J. K. acknowledges Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with Institute of Applied Physics RAS).Peer reviewedPreprin

Recurrence Plots 25 years later -- gaining confidence in dynamical transitions

Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots

Optimal model-free prediction from multivariate time series

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal pre-selection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used sub-optimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure

Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm (Liu \textit{et al.,} Phys. Rev. E \textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatment disregarding the intrinsic non-stationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for non-stationary stochastic processes like fBm.Comment: 8 pages, 6 figure

Collective Relaxation Dynamics of Small-World Networks

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian or a similar linear operator. The structure of networks with regular, small-world and random connectivities are reasonably well understood, but their collective dynamical properties remain largely unknown. Here we present a two-stage mean-field theory to derive analytic expressions for network spectra. A single formula covers the spectrum from regular via small-world to strongly randomized topologies in Watts-Strogatz networks, explaining the simultaneous dependencies on network size N, average degree k and topological randomness q. We present simplified analytic predictions for the second largest and smallest eigenvalue, and numerical checks confirm our theoretical predictions for zero, small and moderate topological randomness q, including the entire small-world regime. For large q of the order of one, we apply standard random matrix theory thereby overarching the full range from regular to randomized network topologies. These results may contribute to our analytic and mechanistic understanding of collective relaxation phenomena of network dynamical systems.Comment: 12 pages, 10 figures, published in PR

Complex Network Approach to the Statistical Features of the Sunspot Series

Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse-transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network which span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15\,--\,1000 days by a power-law regime with scaling exponent $\gamma = 2.04$ of the occurrence time of the two subsequent and successive strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models. The power-law regime suggested by the waiting times does indicate that there are some level of predictable patterns in the minima.Comment: 18 pages, 11 figures. Solar Physics, 201