Estimating covariant Lyapunov vectors from data.

Covariant Lyapunov vectors characterize the directions along which perturbations in dynamical systems grow. They have also been studied as predictors of critical transitions and extreme events. For many applications, it is necessary to estimate these vectors from data since model equations are unknown for many interesting phenomena.

Fluctuation-induced distributed resonances in oscillatory networks.

Across physics, biology, and engineering, the collective dynamics of oscillatory networks often evolve into self-organized operating states. How such networks respond to external fluctuating signals fundamentally underlies their function, yet is not well understood. Here, we present a theory of dynamic network response patterns and reveal how distributed resonance patterns emerge in oscillatory networks once the dynamics of the oscillatory units become more than one-dimensional.

Critical transitions and perturbation growth directions.

Critical transitions occur in a variety of dynamical systems. Here we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors.

Model-free inference of direct network interactions from nonlinear collective dynamics.

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem.

Vocal repertoire of long-finned pilot whales (Globicephala melas) in northern Norway.

The knowledge of the vocal repertoire of pilot whales is very limited. In this paper, the vocal repertoire of long-finned pilot whales recorded during different encounters in the Vestfjord in northern Norway between November 2006 and August 2010 are described. Sounds were analysed using two different methods: (1) an observer-based audio-visual inspection of FFT-derived spectrograms, with which, besides a general variety of clicks, buzzes, nonharmonic sounds, and whistles, 129 different distinct call types and 25 subtypes were distinguished.

Network susceptibilities: Theory and applications.

We introduce the concept of network susceptibilities quantifying the response of the collective dynamics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge susceptibilities, measuring the responses due to changes in the properties of units and their interactions, respectively. We derive explicit forms of network susceptibilities for oscillator networks close to steady states and offer example applications for Kuramoto-type phase-oscillator models, power grid models, and generic flow models.

Critical Links and Nonlocal Rerouting in Complex Supply Networks.

Link failures repeatedly induce large-scale outages in power grids and other supply networks. Yet, it is still not well understood which links are particularly prone to inducing such outages. Here we analyze how the nature and location of each link impact the network's capability to maintain a stable supply.

Quantifying group specificity of animal vocalizations without specific sender information.

Recordings of animal vocalization can lack information about sender and context. This is often the case in studies on marine mammals or in the increasing number of automated bioacoustics monitorings. Here, we develop a framework to estimate group specificity without specific sender information.

Predictability of critical transitions.

Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socioeconomic changes and climate transitions between ice ages and warm ages. From bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition.

Logarithmic bred vectors in spatiotemporal chaos: structure and growth.

Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyapunov vector.

Predicting extreme avalanches in self-organized critical sandpiles.

In a finite-size Abelian sandpile model, extreme avalanches are repelling each other. Taking a time series of the avalanche size and using a decision variable derived from that, we predict the occurrence of a particularly large avalanche in the next time step. The larger the magnitude of these target avalanches, the better is their predictability.

Precursors of extreme increments.

We investigate precursors and the predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of the predictions depends on the strategy to choose precursors, on the size of the event, and on the correlation strength.