Browsing by Author "Bačić, Iva"

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    Disordered configurations of the Glauber model in two-dimensional networks
    Bačić, Iva; Franović, Igor; Perc, Matjaž
    We analyze the ordering efficiency and the structure of disordered configurations for the zero-temperature Glauber model on Watts-Strogatz networks obtained by rewiring 2D regular square lattices. In the small-world regime, the dynamics fails to reach the ordered state in the thermodynamic limit. Due to the interplay of the perturbed regular topology and the energy neutral stochastic state transitions, the stationary state consists of two intertwined domains, manifested as multiclustered states on the original lattice. Moreover, for intermediate rewiring probabilities, one finds an additional source of disorder due to the low connectivity degree, which gives rise to small isolated droplets of spins. We also examine the ordering process in paradigmatic two-layer networks with heterogeneous rewiring probabilities. Comparing the cases of a multiplex network and the corresponding network with random inter-layer connectivity, we demonstrate that the character of the final state qualitatively depends on the type of inter-layer connections.
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    Dynamics of a stochastic excitable system with slowly adapting feedback
    Franović, Igor; Yanchuk, Serhiy; Eydam, Sebastian; Bačić, Iva; Wolfrum, Matthias
    We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic bursting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance or effectively control the features of the stochastic bursting. The setup can be considered a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker–Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting.
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    Impact of Physicality on Network Structure
    Pósfai, Márton; Szegedy, Balázs; Bačić, Iva; Blagojević, Luka; Abért, Miklós; Kertész, János; Lovász, László; Barabási, Albert-László
    The emergence of detailed maps of physical networks, such as the brain connectome, vascular networks or composite networks in metamaterials, whose nodes and links are physical entities, has demonstrated the limits of the current network science toolset. Link physicality imposes a non-crossing condition that affects both the evolution and the structure of a network, in a way that the adjacency matrix alone—the starting point of all graph-based approaches—cannot capture. Here, we introduce a meta-graph that helps us to discover an exact mapping between linear physical networks and independent sets, which is a central concept in graph theory. The mapping allows us to analytically derive both the onset of physical effects and the emergence of a jamming transition, and to show that physicality affects the network structure even when the total volume of the links is negligible. Finally, we construct the meta-graphs of several real physical networks, which allows us to predict functional features, such as synapse formation in the brain connectome, that agree with empirical data. Overall, our results show that, to understand the evolution and behaviour of real complex networks, the role of physicality must be fully quantified.
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    Inverse stochastic resonance in a system of excitable active rotators with adaptive coupling
    Bačić, Iva; Klinshov, Vladimir; Nekorkin, Vladimir; Perc, Matjaž; Franović, Igor
    Inverse stochastic resonance is a phenomenon where an oscillating system influenced by noise exhibits a minimal oscillation frequency at an intermediate noise level. We demonstrate a novel generic scenario for such an effect in a multi-timescale system, considering an example of emergent oscillations in two adaptively coupled active rotators with excitable local dynamics. The impact of plasticity turns out to be twofold. First, at the level of multiscale dynamics, one finds a range of intermediate adaptivity rates that give rise to multistability between the limit cycle attractors and the stable equilibria, a condition necessary for the onset of the effect. Second, applying the fast-slow analysis, we show that the plasticity also plays a facilitatory role on a more subtle level, guiding the fast flow dynamics to parameter domains where the stable equilibria become focuses rather than nodes, which effectively enhances the influence of noise. The described scenario persists for different plasticity rules, underlying its robustness in the light of potential applications to neuroscience and other types of cell dynamics.
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    Two paradigmatic scenarios for inverse stochastic resonance
    Bačić, Iva; Franović, Igor
    Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold. In the first scenario, shown for the two rotators in the excitable regime, inverse stochastic resonance emerges due to a biased switching between the oscillatory and the quasi-stationary metastable states derived from the attractors of the noiseless system. In the second scenario, illustrated for the rotators in the oscillatory regime, inverse stochastic resonance arises due to a trapping effect associated with a noise-enhanced stability of an unstable fixed point. The details of the mechanisms behind the resonant effect are explained in terms of slow–fast analysis of the corresponding noiseless systems.