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- ItemChanges in meandering of the Northern Hemisphere circulation(Bristol : Institute of Physics Publishing, 2016) Di Capua, G.; Coumou, D.
- ItemControl of transversal instabilities in reaction-diffusion systems(Bristol : Institute of Physics Publishing, 2018) Totz, S.; Löber, J.; Totz, J.F.; Engel, H.In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh-Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov-Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.
- ItemInterval stability for complex systems(Bristol : Institute of Physics Publishing, 2018) Klinshov, V.V.; Kirillov, S.; Kurths, J.; Nekorkin, V.I.Stability of dynamical systems against strong perturbations is an important problem of nonlinear dynamics relevant to many applications in various areas. Here, we develop a novel concept of interval stability, referring to the behavior of the perturbed system during a finite time interval. Based on this concept, we suggest new measures of stability, namely interval basin stability (IBS) and interval stability threshold (IST). IBS characterizes the likelihood that the perturbed system returns to the stable regime (attractor) in a given time. IST provides the minimal magnitude of the perturbation capable to disrupt the stable regime for a given interval of time. The suggested measures provide important information about the system susceptibility to external perturbations which may be useful for practical applications. Moreover, from a theoretical viewpoint the interval stability measures are shown to bridge the gap between linear and asymptotic stability. We also suggest numerical algorithms for quantification of the interval stability characteristics and demonstrate their potential for several dynamical systems of various nature, such as power grids and neural networks.
- ItemImproving power grid transient stability by plug-in electric vehicles(Bristol : Institute of Physics Publishing, 2014) Gajduk, A.; Todorovski, M.; Kurths, J.; Kocarev, L.Plug-in electric vehicles (PEVs) can serve in discharge mode as distributed energy and power resources operating as vehicle-to-grid (V2G) devices and in charge mode as loads or grid-to-vehicle devices. It has been documented that PEVs serving as V2G systems can offer possible backup for renewable power sources, can provide reactive power support, active power regulation, load balancing, peak load shaving, can reduce utility operating costs and can generate revenue. Here we show that PEVs can even improve power grid transient stability, that is, stability when the power grid is subjected to large disturbances, including bus faults, generator and branch tripping, and sudden large load changes. A control strategy that regulates the power output of a fleet of PEVs based on the speed of generator turbines is proposed and tested on the New England 10-unit 39-bus power system. By regulating the power output of the PEVs we show that (1) speed and voltage fluctuations resulting from large disturbances can be significantly reduced up to five times, and (2) the critical clearing time can be extended by 20-40%. Overall, the PEVs control strategy makes the power grid more robust.
- ItemStability threshold approach for complex dynamical systems(Bristol : Institute of Physics Publishing, 2016) Klinshov, V.V.; Nekorkin, V.I.; Kurths, J.
- ItemGeneral scaling of maximum degree of synchronization in noisy complex networks(Bristol : Institute of Physics Publishing, 2014) Traxl, D.; Boers, N.; Kurths, J.The effects of white noise and global coupling strength on the maximum degree of synchronization in complex networks are explored. We perform numerical simulations of generic oscillator models with both linear and non-linear coupling functions on a broad spectrum of network topologies. The oscillator models include the Fitzhugh-Nagumo model, the Izhikevich model and the Kuramoto phase oscillator model. The network topologies range from regular, random and highly modular networks to scale-free and small-world networks, with both directed and undirected edges. We then study the dependency of the maximum degree of synchronization on the global coupling strength and the noise intensity. We find a general scaling of the synchronizability, and quantify its validity by fitting a regression model to the numerical data.
- ItemQuantum collapse rules from the maximum relative entropy principle(Bristol : Institute of Physics Publishing, 2016) Hellmann, F.; Kamiński, W.; Kostecki, R.P.
- ItemDetours around basin stability in power networks(Bristol : Institute of Physics Publishing, 2014) Schultz, P.; Heitzig, J.; Kurths, J.To analyse the relationship between stability against large perturbations and topological properties of a power transmission grid, we employ a statistical analysis of a large ensemble of synthetic power grids, looking for significant statistical relationships between the single-node basin stability measure and classical as well as tailormade weighted network characteristics. This method enables us to predict poor values of single-node basin stability for a large extent of the nodes, offering a node-wise stability estimation at low computational cost. Further, we analyse the particular function of certain network motifs to promote or degrade the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design.
- ItemCartesian product of synchronization transitions and hysteresis(Bristol : Institute of Physics Publishing, 2017) Wang, C.; Zou, Y.; Guan, S.; Kurths, J.We present theoretical results when applying the Cartesian product of two Kuramoto models on different network topologies. By a detailed mathematical analysis, we prove that the dynamics on the Cartesian product graph can be described by the canonical equations as the Kuramoto model. We show that the order parameter of the Cartesian product is the product of the order parameters of the factors. On the product graph, we observe either continuous or discontinuous synchronization transitions. In addition, under certain conditions, the transition from an initially incoherent state to a coherent one is discontinuous, while the transition from a coherent state to an incoherent one is continuous, presenting a mixture state of first and second order synchronization transitions. Our numerical results are in a good agreement with the theoretical predictions. These results provide new insight for network design and synchronization control.
- ItemTiming of transients: Quantifying reaching times and transient behavior in complex systems(Bristol : Institute of Physics Publishing, 2017) Kittel, T.; Heitzig, J.; Webster, K.; Kurths, J.In dynamical systems, one may ask how long it takes for a trajectory to reach the attractor, i.e. how long it spends in the transient phase. Although for a single trajectory the mathematically precise answer may be infinity, it still makes sense to compare different trajectories and quantify which of them approaches the attractor earlier. In this article, we categorize several problems of quantifying such transient times. To treat them, we propose two metrics, area under distance curve and regularized reaching time, that capture two complementary aspects of transient dynamics. The first, area under distance curve, is the distance of the trajectory to the attractor integrated over time. It measures which trajectories are 'reluctant', i.e. stay distant from the attractor for long, or 'eager' to approach it right away. Regularized reaching time, on the other hand, quantifies the additional time (positive or negative) that a trajectory starting at a chosen initial condition needs to approach the attractor as compared to some reference trajectory. A positive or negative value means that it approaches the attractor by this much 'earlier' or 'later' than the reference, respectively. We demonstrated their substantial potential for application with multiple paradigmatic examples uncovering new features.