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Author: Wolfrum, Matthias × Start date: 1990 × DDC: 510 × Has files: Yes × Subject: large delay ×

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Now showing 1 - 5 of 5
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    Oscillatory instability in systems with delay
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Wolfrum, Matthias; Yanchuk, Serhiy
    Any biological or physical system, which incorporates delayed feedback or delayed coupling, can be modeled by a dynamical system with delayed argument. We describe a standard oscillatory destabilization mechanism, which occurs in such systems.
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    Control of unstable steady states by strongly delayed feedback
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Yanchuk, Serhiy; Wolfrum, Matthias; Hövel, Philipp; Schöll, Eckehard
    We present an asymptotic analysis of time-delayed feedback control of steady states for large delay time. By scaling arguments, and a detailed comparison with exact solutions, we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type. Insight into the control mechanism is gained by analysing the eigenvalue spectrum, which consists of a pseudo-continuous spectrum and up to two strongly unstable eigenvalues. Although the standard control scheme generally fails for large delay, we find that if the uncontrolled system is sufficiently close to its instability threshold, control does work even for relatively large delay times.
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    Spectrum and amplitude equations for scalar delay-differential equations with large delay
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Yanchuk, Serhiy; Lücken, Leonhard; Wolfrum, Matthias; Mielke, Alexander
    The subject of the paper are scalar delay-differential equations with large delay. Firstly, we describe the asymptotic properties of the spectrum of linear equations. Using these properties, we classify possible types of destabilization of steady states. In the limit of large delay, this classification is similar to the one for parabolic partial differential equations. We present a derivation and error estimates for amplitude equations, which describe universally the local behavior of scalar delay-differential equations close to the destabilization threshold.
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    On the stability of periodic orbits in delay equations with large delay
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Sieber, Jan; Wolfrum, Matthias; Lichtner, Mark; Yanchuk, Serhiy
    We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set of curves, which we call asymptotic continuous spectrum, that is independent on the delay
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    Multiple self-locking in the Kuramoto--Sakaguchi system with delay
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Wolfrum, Matthias; Yanchuk, Serhiy; D'Huys, Otti
    We study the Kuramoto-Sakaguchi system of phase oscillators with a delayed mean-field coupling. By applying the theory of large delay to the corresponding Ott--Antonsen equation, we explain fully analytically the mechanisms for the appearance of multiple coexisting partially locked states. Closely above the onset of synchronization, these states emerge in the Eckhaus scenario: with increasing coupling, more and more partially locked states appear unstable from the incoherent state, and gain stability for larger coupling at a modulational stability boundary. The partially locked states with strongly detuned frequencies are shown to emerge subcritical and gain stability only after a fold and a series of Hopf bifurcations. We also discuss the role of the Sakaguchi phase lag parameter. For small delays, it determines, together with the delay time, the attraction or repulsion to the central frequency, which leads to supercritical or subcritical behavior, respectively. For large delay, the Sakaguchi parameter does not influence the global dynamical scenario.