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Type: Report × Subject: bifurcation analysis ×

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Now showing 1 - 3 of 3
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    Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Omel'chenko, Oleh
    We consider a paradigmatic spatially extended model of non-locally coupled phase oscillators which are uniformly distributed within a one-dimensional interval and interact depending on the distance between their sites modulo periodic boundary conditions. This model can display peculiar spatio-temporal patterns consisting of alternating patches with synchronized (coherent) or irregular (incoherent) oscillator dynamics, hence the name coherence-incoherence pattern, or chimera state. For such patterns we formulate a general bifurcation analysis scheme based on a hierarchy of continuum limit equations. This gives us possibility to classify known coherence-incoherence patterns and to suggest directions for searching new ones
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    Dynamical regimes of multi-stripe laser array with external off-axis feedback
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Pimenov, Alexander; Trpmciu, Vasile Z.; Bandelow, Uwe; Vladimirov, Andrei G.
    We study theoretically the dynamics of a multistripe laser array with an external cavity formed by either a single or two off-axis feedback mirrors, which allow to select a single lateral mode with transversely modulated intensity distribution. We derive and analyze a reduced model of such an array based on a set of delay differential equations taking into account transverse carrier grating in the semiconductor medium. With the help of the bifurcation analysis of the reduced model we show the existence of single and multimode instabilities leading to periodic and irregular pulsations of the output intensity. In particular, we observe a multimode instability leading to a periodic regime with anti-phase oscillating intensities of the two counter-propagating waves in the external cavity. This is in agreement with the result obtained earlier with the help of a 2+1 dimensional traveling wave model
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    Stability of spiral chimera states on a torus
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Omelchenko, Oleh E.; Wolfrum, Matthias; Knobloch, Edgar
    We study destabilization mechanisms of spiral coherence-incoherence patterns known as spiral chimera states that form on a two-dimensional lattice of nonlocally coupled phase oscillators. For this purpose we employ the linearization of the OttAntonsen equation that is valid in the continuum limit and perform a detailed two-parameter stability analysis of a D4-symmetric chimera state, i.e., a four-core spiral state. We identify fold, Hopf and parity-breaking bifurcations as the main mechanisms whereby spiral chimeras can lose stability. Beyond these bifurcations we find new spatio-temporal patterns, in particular, quasiperiodic chimeras, D2-symmetric spiral chimeras as well as drifting states.