Filters

2020 - 20224

More filters

2021 - 20234
Reset filters

Settings

search.filters.applied.f.access: openAccess × Author: Hellmann, Frank × End date: 2023 × Start date: 2020 ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Network-induced multistability through lossy coupling and exotic solitary states
    ([London] : Nature Publishing Group UK, 2020) Hellmann, Frank; Schultz, Paul; Jaros, Patrycja; Levchenko, Roman; Kapitaniak, Tomasz; Kurths, Jürgen; Maistrenko, Yuri
    The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. For these, the ongoing transition to distributed renewable energy sources leads to a proliferation of dynamical actors. The desynchronisation of a few or even one of those would likely result in a substantial blackout. Thus the dynamical stability of the synchronous state has become a leading topic in power grid research. Here we uncover that, when taking into account physical losses in the network, the back-reaction of the network induces new exotic solitary states in the individual actors and the stability characteristics of the synchronous state are dramatically altered. These effects will have to be explicitly taken into account in the design of future power grids. We expect the results presented here to transfer to other systems of coupled heterogeneous Newtonian oscillators.
  • Thumbnail Image
    Item
    Moving the epidemic tipping point through topologically targeted social distancing
    (Berlin ; Heidelberg : Springer, 2021) Ansari, Sara; Anvari, Mehrnaz; Pfeffer, Oskar; Molkenthin, Nora; Moosavi, Mohammad R.; Hellmann, Frank; Heitzig, Jobst; Kurths, Jürgen
    The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. The MCMC method generates samples from the relative canonical network ensemble with a defined expectation value of λmax . We call this the "well-controlling network ensemble" (WCNE) and compare its structure to randomly thinned networks with the same link density. We observe that networks in the WCNE tend to be more homogeneous in the degree distribution and use this insight to define two ad-hoc removal strategies, which also substantially reduce the largest eigenvalue. A targeted removal of 80% of links can be as effective as a random removal of 90%, leaving individuals with twice as many contacts. Finally, by simulating epidemic spreading via either an SIS or an SIR model on network ensembles created with different link removal strategies (random, WCNE, or degree-homogenizing), we show that tipping from an epidemic to a non-epidemic state happens at a larger critical ratio between infection rate and recovery rate for WCNE and degree-homogenized networks than for those obtained by random removals.
  • Thumbnail Image
    Item
    Ensemble analysis of complex network properties—an MCMC approach
    ([London] : IOP, 2022) Pfeffer, Oskar; Molkenthin, Nora; Hellmann, Frank
    What do generic networks that have certain properties look like? We use relative canonical network ensembles as the ensembles that realize a property R while being as indistinguishable as possible from a background network ensemble. This allows us to study the most generic features of the networks giving rise to the property under investigation. To test the approach we apply it to study properties thought to characterize ‘small-world networks’. We consider two different defining properties, the ‘small-world-ness’ of Humphries and Gurney, as well as a geometric variant. Studying them in the context of Erdős-Rényi and Watts-Strogatz ensembles we find that all ensembles studied exhibit phase transitions to systems with large hubs and in some cases cliques. Such features are not present in common examples of small-world networks, indicating that these properties do not robustly capture the notion of small-world networks. We expect the overall approach to have wide applicability for understanding network properties of real world interest, such as optimal ride-sharing designs, the vulnerability of networks to cascades, the performance of communication topologies in coordinating fluctuation response or the ability of social distancing measures to suppress disease spreading.
  • Thumbnail Image
    Item
    Monte Carlo basin bifurcation analysis
    ([London] : IOP, 2020) Gelbrecht, Maximilian; Kurths, Jürgen; Hellmann, Frank
    Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds-Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart-Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.