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- ItemInfluence of Sound on Empirical Brain Networks(Lausanne : Frontiers Media, 2021) Sawicki, Jakub; Schöll, EckehardWe analyze the influence of an external sound source in a network of FitzHugh–Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report synchronization patterns, induced by the frequency of the sound source. We show that the level of synchrony can be enhanced by choosing the frequency of the sound source and its amplitude as control parameters for synchronization patterns. We discuss a minimum model elucidating the modalities of the influence of music on the human brain.
- ItemEmbedding the dynamics of a single delay system into a feed-forward ring(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Klinshov, Vladimir; Shchapin, Dmitry; Yanchuk, Serhiy; Wolfrum, Matthias; D'Huys, Otti; Nekorkin, VladimirWe investigate the relation between the dynamics of a single oscillator with delayed selffeedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings. We discover several cases where stability of periodic solution for the single unit can be related to the stability of the corresponding rotating wave in the ring. As a specific example we demonstrate how the complex bifurcation scenario of simultaneously emerging multi-jittering solutions can be transferred from a single oscillator with delayed pulse feedback to multi-jittering rotating waves in a sufficiently large ring of oscillators with instantaneous pulse coupling. Finally, we present an experimental realization of this dynamical phenomenon in a system of coupled electronic circuits of FitzHughNagumo type.
- ItemBifurcations in the Sakaguchi-Kuramoto model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Omel'chenko, Oleh; Wolfrum, MatthiasWe analyze the Sakaguchi-Kuramoto model of coupled phase oscillators in a continuum limit given by a frequency dependent version of the Ott-Antonsen system. Based on a self-consistency equation, we provide a detailed analysis of partially synchronized states, their bifurcation from the completely incoherent state and their stability properties. We use this method to analyze the bifurcations for various types of frequency distributions and explain the appearance of non-universal synchronization transitions.