Journal: Chaos

Abbreviation

Chaos

Publisher

American Institute of Physics

Journal Volumes

ISSN

1054-1500
1089-7682

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Publications 1 - 10 of 61
  • Global variational approach to elliptic transport barriers in three dimensions
    Item type: Journal Article
    Oettinger, David; Blazevski, Daniel; Haller, George (2016)
    Chaos
  • Rumor spreading: A trigger for proliferation or fading away
    Item type: Journal Article
    Zehmakan, Ahad N.; Galam, Serge (2020)
    Chaos
    The dynamics of rumor spreading is investigated using a model with three kinds of agents who are, respectively, the Seeds, the Agnostics, and the Others. While Seeds are the ones who start spreading the rumor being adamantly convinced of its truth, Agnostics reject any kind of rumor and do not believe in conspiracy theories. In between, the Others constitute the main part of the community. While Seeds are always Believers and Agnostics are always Indifferents, Others can switch between being Believer and Indifferent depending on who they are discussing with. The underlying driving dynamics is implemented via local updates of randomly formed groups of agents. In each group, an Other turns into a Believer as soon as m or more Believers are present in the group. However, since some Believers may lose interest in the rumor as time passes by, we add a flipping fixed rate 0 < d < 1 from Believers into Indifferents. Rigorous analysis of the associated dynamics reveals that switching from m = 1 to m ≥ 2 triggers a drastic qualitative change in the spreading process. When m = 1, even a small group of Believers may manage to convince a large part of the community very quickly. In contrast, for m ≥ 2, even a substantial fraction of Believers does not prevent the rumor dying out after a few update rounds. Our results provide an explanation on why a given rumor spreads within a social group and not in another and also why some rumors will not spread in neither groups.
  • Nonlinear model reduction to fractional and mixed-mode spectral submanifolds
    Item type: Journal Article
    Haller, George; Kaszás, Bálint; Liu, Aihui; et al. (2023)
    Chaos
    A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace E of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an attracting primary SSM provides a mathematically precise reduction of the full system dynamics to a very low-dimensional, smooth model in polynomial form. A limitation of this model reduction approach has been, however, that the spectral subspace yielding the SSM must be spanned by eigenvectors of the same stability type. A further limitation has been that in some problems, the nonlinear behavior of interest may be far away from the smoothest nonlinear continuation of the invariant subspace E. Here, we remove both of these limitations by constructing a significantly extended class of SSMs that also contains invariant manifolds with mixed internal stability types and of lower smoothness class arising from fractional powers in their parametrization. We show on examples how fractional and mixed-mode SSMs extend the power of data-driven SSM reduction to transitions in shear flows, dynamic buckling of beams, and periodically forced nonlinear oscillatory systems. More generally, our results reveal the general function library that should be used beyond integer-powered polynomials in fitting nonlinear reduced-order models to data.
  • Quasi-objective eddy visualization from sparse drifter data
    Item type: Journal Article
    Encinas-Bartos, Alex P.; Aksamit, Nikolas O.; Haller, George (2022)
    Chaos
    We employ a recently developed single-trajectory Lagrangian diagnostic tool, the trajectory rotation average (TRA over bar ), to visualize oceanic vortices (or eddies) from sparse drifter data. We apply the TRA over bar to two drifter data sets that cover various oceanographic scales: the Grand Lagrangian Deployment and the Global Drifter Program. Based on the TRA over bar , we develop a general algorithm that extracts approximate eddy boundaries. We find that the TRA over bar outperforms other available single-trajectory-based eddy detection methodologies on sparse drifter data and identifies eddies on scales that are unresolved by satellite-altimetry. Published under an exclusive license by AIP Publishing.
  • Inter-role reciprocity in evolutionary trust game on square lattices
    Item type: Journal Article
    Wang, Chaoqian; Zhang, Wei; Wang, Xinwei; et al. (2025)
    Chaos
    Simulating bipartite games, such as the trust game, is not straightforward due to the lack of a natural way to distinguish roles in a single population. The square lattice topology can provide a simple yet elegant solution by alternating trustors and trustees. For even lattice sizes, it creates two disjoint diagonal sub-lattices for strategy learning, while game interactions can take place on the original lattice. This setup ensures a minimal spatial structure that allows interactions across roles and learning within roles. By simulations on this setup, we detect an inter-role spatial reciprocity mechanism, through which trust can emerge. In particular, a moderate return ratio allows investing trustors and trustworthy trustees to form inter-role clusters and thus save trust. If the return is too high, it harms the survival of trustees; if too low, it harms trustors. The proposed simulation framework is also applicable to any bipartite game to uncover potential inter-role spatial mechanisms across various scenarios.
  • Eluding oblivion with smart stochastic selection of synaptic updates
    Item type: Journal Article
    Fusi, Stefano; Senn, Walter (2006)
    Chaos
  • Dynamical equivalence between Kuramoto models with first- and higher-order coupling
    Item type: Journal Article
    Delabays, Robin (2019)
    Chaos
  • Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties
    Item type: Journal Article
    Delabays, Robin; Tyloo, Melvyn; Jacquod, Philippe (2019)
    Chaos
  • Chaotic synchronization of spatially extended systems as non-equilibrium phase transitions
    Item type: Journal Article
    Cencini, Massimo; Tessone, Claudio J.; Torcini, Alessandro (2008)
    Chaos
  • Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks
    Item type: Journal Article
    Lombardi, Fabrizio; Herrmann, Hans J.; de Arcangelis, Lucilla (2017)
    Chaos
    The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.
Publications 1 - 10 of 61