59 research outputs found

    Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

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    We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.Comment: postprint, as accepted in Chaos, 10 pages, 7 figure

    A Tweezer for Chimeras in Small Networks

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    We propose a control scheme which can stabilize and fix the position of chimera states in small networks. Chimeras consist of coexisting domains of spatially coherent and incoherent dynamics in systems of nonlocally coupled identical oscillators. Chimera states are generally difficult to observe in small networks due to their short lifetime and erratic drifting of the spatial position of the incoherent domain. The control scheme, like a tweezer, might be useful in experiments, where usually only small networks can be realized

    Periodic solutions in next generation neural field models

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    We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial location are described by a complex-valued Riccati equation we derive a self-consistency equation that such periodic solutions must satisfy. We determine the stability of these solutions, and present numerical results to illustrate the usefulness of this technique. The generality of this approach is demonstrated through its application to several other systems involving delays, two-population architecture and networks of Winfree oscillators.Comment: 15 pages, 11 figure

    Bumps, chimera states, and Turing patterns in systems of coupled active rotators

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    Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units similar patterns, where coherent units are at rest, are called bump states. Here, we study bumps in an array of active rotators coupled by non-local attraction and global repulsion. We demonstrate how they can emerge in a supercritical scenario from completely coherent Turing patterns: single incoherent units appear in a homoclinic bifurcation with a subsequent transition via quasiperiodic and chaotic behavior, eventually transforming into extensive chaos with many incoherent units. We present different types of transitions and explain the formation of coherence-incoherence patterns according to the classical paradigm of short-range activation and long-range inhibition

    Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions

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    Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bifurcations of twisted states in ring networks of phase oscillators with nonpairwise higher-order interactions. Hopf bifurcations give rise to quasiperiodic solutions that move along the oscillator ring at nontrivial speed. Because of the higher-order interactions, these emerging solutions may be stable. Using the Ott--Antonsen approach, we continue the emergent solution branches which approach anti-phase type solutions (where oscillators form two clusters whose phase is π\pi apart) as well as twisted states with a different winding number.Comment: 24 pages, 8 figure

    The politics of in/visibility: carving out queer space in Ul'yanovsk

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    <p>In spite of a growing interest within sexualities studies in the concept of queer space (Oswin 2008), existing literature focuses almost exclusively on its most visible and territorialised forms, such as the gay scene, thus privileging Western metropolitan areas as hubs of queer consumer culture (Binnie 2004). While the literature has emphasised the political significance of queer space as a site of resistance to hegemonic gender and sexual norms, it has again predominantly focused on overt claims to public space embodied in Pride events, neglecting other less open forms of resistance.</p><p> This article contributes new insights to current debates about the construction and meaning of queer space by considering how city space is appropriated by an informal queer network in Ul’ianovsk. The group routinely occupied very public locations meeting and socialising on the street or in mainstream cafĂ©s in central Ul’ianovsk, although claims to these spaces as queer were mostly contingent, precarious or invisible to outsiders. The article considers how provincial location affects tactics used to carve out communal space, foregrounding the importance of local context and collective agency in shaping specific forms of resistance, and questioning ethnocentric assumptions about the empowering potential of visibility.</p&gt
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