Weighted networks are more synchronizable: how and why

Most real-world networks display not only a heterogeneous distribution of degrees, but also a heterogeneous distribution of weights in the strengths of the connections. Each of these heterogeneities alone has been shown to suppress synchronization in random networks of dynamical systems. Here we review our recent findings that complete synchronization is significantly enhanced and becomes independent of both distributions when the distribution of weights is suitably combined with the distribution of degrees. We also present new results addressing the optimality of our findings and extending our analysis to phase synchronization in networks of non-identical dynamical units.Comment: Proceedings of the CNET 2004 (29 August - 2 September 2004

Timing of Transients : Quantifying Reaching Times and Transient Behavior in Complex Systems

The authors thank the anonymous referees for their detailed and constructive feedback. This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. This work was conducted in the framework of PIK’s flagship project on coevolutionary pathways (copan). The authors thank CoNDyNet (FKZ 03SF0472A) for their cooperation. The authors gratefully acknowledge the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research. The authors thank the developers of the used software: Python[47], Numerical Python[48] and Scientific Python[49]. The authors thank Sabine Auer, Karsten Bolts, Catrin Ciemer, Jonathan Donges, Reik Donner, Jasper Franke, Frank Hellmann, Jakob Kolb, Chiranjit Mitra, Finn Muller-Hansen, Jan Nitzbon, Anton Plietzsch Stefan Ruschel, Tiago Pereira da Silva, Francisco A. Rodrigues, Paul Schultz, and Lyubov Tupikina for helpful discussions and comments.Peer reviewedPublisher PD

Impact of leader on cluster synchronization

5 pages, 5 figuresNon peer reviewedPostprin

Generalizing the transition from amplitude to oscillation death in coupled oscillators

Peer reviewedPublisher PD

Transition from homogeneous to inhomogeneous limit cycles : Effect of local filtering in coupled oscillators

10 pages, 8 FigsPeer reviewedPublisher PD

Rapidly switched random links enhance spatiotemporal regularity

We investigate the spatiotemporal properties of a lattice of chaotic maps whose coupling connections are rewired to random sites with probability p. Keeping p constant, we change the random links at different frequencies in order to discern the effect (if any) of the time dependence of the links. We observe two different regimes in this network: (i) when the network is rewired slowly, namely, when the random connections are quite static, the dynamics of the network is spatiotemporally chaotic and (ii) when these random links are switched around fast, namely, the network is rewired frequently, one obtains a spatiotemporal fixed point over a large range of coupling strengths. We provide evidence of a sharp transition from a globally attracting spatiotemporal fixed point to spatiotemporal chaos as the rewiring frequency is decreased. Thus, in addition to geometrical properties such as the fraction of random links in the network, dynamical information on the time dependence of these links is crucial in determining the spatiotemporal properties of complex dynamical networks

Recurrence networks - A novel paradigm for nonlinear time series analysis

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases. It is demonstrated that there are fundamental relationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis

Sleep apnea-hypopnea quantification by cardiovascular data analysis

Sleep apnea is the most common sleep disturbance and it is an important risk factor for cardiovascular disorders. Its detection relies on a polysomnography, a combination of diverse exams. In order to detect changes due to sleep disturbances such as sleep apnea occurrences, without the need of combined recordings, we mainly analyze systolic blood pressure signals (maximal blood pressure value of each beat to beat interval). Nonstationarities in the data are uncovered by a segmentation procedure, which provides local quantities that are correlated to apnea-hypopnea events. Those quantities are the average length and average variance of stationary patches. By comparing them to an apnea score previously obtained by polysomnographic exams, we propose an apnea quantifier based on blood pressure signal. This furnishes an alternative procedure for the detection of apnea based on a single time series, with an accuracy of 82%