TY - JOUR A1 - Anishchenko, Vadim S. A1 - Nikolaev, S A1 - Kurths, Jürgen T1 - Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions N2 - We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.056202 SN - 1539-3755 ER - TY - JOUR A1 - Agarwal, Ankit A1 - Maheswaran, Rathinasamy A1 - Marwan, Norbert A1 - Caesar, Levke A1 - Kurths, Jürgen T1 - Wavelet-based multiscale similarity measure for complex networks JF - The European physical journal : B, Condensed matter and complex systems N2 - In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales. KW - Statistical and Nonlinear Physics Y1 - 2018 U6 - https://doi.org/10.1140/epjb/e2018-90460-6 SN - 1434-6028 SN - 1434-6036 VL - 91 IS - 11 PB - Springer CY - New York ER - TY - JOUR A1 - Agarwal, Ankit A1 - Maheswaran, Rathinasamy A1 - Kurths, Jürgen A1 - Khosa, R. T1 - Wavelet Spectrum and Self-Organizing Maps-Based Approach for Hydrologic Regionalization -a Case Study in the Western United States JF - Water Resources Management N2 - Hydrologic regionalization deals with the investigation of homogeneity in watersheds and provides a classification of watersheds for regional analysis. The classification thus obtained can be used as a basis for mapping data from gauged to ungauged sites and can improve extreme event prediction. This paper proposes a wavelet power spectrum (WPS) coupled with the self-organizing map method for clustering hydrologic catchments. The application of this technique is implemented for gauged catchments. As a test case study, monthly streamflow records observed at 117 selected catchments throughout the western United States from 1951 through 2002. Further, based on WPS of each station, catchments are classified into homogeneous clusters, which provides a representative WPS pattern for the streamflow stations in each cluster. KW - Wavelet power spectrum KW - Regionalization KW - Ungauged catchments KW - K-means technique KW - Self-organizing map Y1 - 2016 U6 - https://doi.org/10.1007/s11269-016-1428-1 SN - 0920-4741 SN - 1573-1650 VL - 30 SP - 4399 EP - 4413 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Kliem, Bernhard A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Dennis, Brian A1 - Schwartz, Richard A1 - Aschwanden, Markus J. T1 - Wavelet analysis of solar flare hard X-ray Y1 - 1998 SN - 0004-637x ER - TY - JOUR A1 - Maheswaran, Rathinasamy A1 - Agarwal, Ankit A1 - Sivakumar, Bellie A1 - Marwan, Norbert A1 - Kurths, Jürgen T1 - Wavelet analysis of precipitation extremes over India and teleconnections to climate indices JF - Stochastic Environmental Research and Risk Assessment N2 - Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Nino 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Nino 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region. KW - Extreme precipitation KW - Teleconnection patterns KW - Wavelets KW - Partial wavelet coherence KW - India Y1 - 2019 U6 - https://doi.org/10.1007/s00477-019-01738-3 SN - 1436-3240 SN - 1436-3259 VL - 33 IS - 11-12 SP - 2053 EP - 2069 PB - Springer CY - New York ER - TY - JOUR A1 - Zaikin, Alexei A. A1 - López, L A1 - Baltanás, J. P. A1 - Kurths, Jürgen A1 - Sanjuan, Miguel Angel Fernández T1 - Vibrational resonance in noise-induced structure N2 - We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise- induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit. Y1 - 2002 UR - http://link.aps.org/abstract/PRE/v66/e011106 ER - TY - JOUR A1 - Gandhimathi, V. M. A1 - Rajasekar, S. A1 - Kurths, Jürgen T1 - Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators JF - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved. KW - vibrational resonance KW - low-frequency force KW - high-frequency force KW - stochastic resonance KW - noise KW - mean residence time Y1 - 2006 U6 - https://doi.org/10.1016/j.physleta.2006.08.051 SN - 0375-9601 VL - 360 IS - 2 SP - 279 EP - 286 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Viana, R. L. A1 - Grebogi, Celso A1 - Pinto, Seds A1 - Lopes, S. R. A1 - Batista, A. M. A1 - Kurths, Jürgen T1 - Validity of numerical trajectories in the synchronization transition of complex systems N2 - We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties Y1 - 2003 SN - 1063-651X ER - TY - JOUR A1 - Baptista, Murilo da Silva A1 - Pereira, Tiago A1 - Kurths, Jürgen T1 - Upper bounds in phase synchronous weak coherent chaotic attractors N2 - An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/01672789 U6 - https://doi.org/10.1016/j.physd.2006.02.007 SN - 0167-2789 ER - TY - JOUR A1 - Beim Graben, Peter A1 - Saddy, Douglas A1 - Kurths, Jürgen T1 - Untitled Y1 - 2004 ER -