Browsing by Author "Zakharova, Anna"

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    Scale-free avalanches in arrays of FitzHugh–Nagumo oscillators
    Contreras, Max; Medeiros, Everton; Zakharova, Anna; Hövel, Philipp; Franović, Igor
    The activity in the brain cortex remarkably shows a simultaneous presence of robust collective oscillations and neuronal avalanches, where intermittent bursts of pseudo-synchronous spiking are interspersed with long periods of quiescence. The mechanisms allowing for such coexistence are still a matter of an intensive debate. Here, we demonstrate that avalanche activity patterns can emerge in a rather simple model of an array of diffusively coupled neural oscillators with multiple timescale local dynamics in the vicinity of a canard transition. The avalanches coexist with the fully synchronous state where the units perform relaxation oscillations. We show that the mechanism behind the avalanches is based on an inhibitory effect of interactions, which may quench the spiking of units due to an interplay with the maximal canard. The avalanche activity bears certain heralds of criticality, including scale-invariant distributions of event sizes. Furthermore, the system shows increased sensitivity to perturbations, manifested as critical slowing down and reduced resilience.
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    Unbalanced clustering and solitary states in coupled excitable systems
    Franović, Igor; Eydam, Sebastian; Semenova, Nadezhda; Zakharova, Anna
    We discover the mechanisms of emergence and the link between two types of symmetry-broken states, the unbalanced periodic two-cluster states and solitary states, in coupled excitable systems with attractive and repulsive interactions. The prevalent solitary states in non-locally coupled arrays, whose self-organization is based on successive (order preserving) spiking of units, derive their dynamical features from the corresponding unbalanced cluster states in globally coupled networks. Apart from the states with successive spiking, we also find cluster and solitary states where the interplay of excitability and local multiscale dynamics gives rise to so-called leap-frog activity patterns with an alternating order of spiking between the units. We show that the noise affects the system dynamics by suppressing the multistability of cluster states and by inducing pattern homogenization, transforming solitary states into patterns of patched synchrony.