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- B Fiedler, V Flunkert, M Georgi, P Hövel, E Schöll
- Physical review letters
- 2007

We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation, which has a… (More)

- Iryna Omelchenko, Oleh E Omel'chenko, Philipp Hövel, Eckehard Schöll
- Physical review letters
- 2013

Systems of nonlocally coupled oscillators can exhibit complex spatiotemporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of these states, found in a widely used model of a limit-cycle oscillator if one goes beyond the limit of weak coupling… (More)

We systematically study the growth kinetics and the critical surface dynamics of cell monolayers by a class of computationally efficient cellular automaton models avoiding lattice artifacts. Our numerically derived front velocity relationship indicates the limitations of the Fisher-Kolmogorov-Petrovskii-Piskounov equation for tumor growth simulations. The… (More)

- Chol-Ung Choe, Thomas Dahms, Philipp Hövel, Eckehard Schöll
- Physical review. E, Statistical, nonlinear, and…
- 2010

We study synchronization in delay-coupled oscillator networks using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of supercritical or subcritical Hopf bifurcation), we derive analytical stability conditions and demonstrate that by tuning the coupling phase one can easily control the stability of… (More)

- Iryna Omelchenko, Yuri Maistrenko, Philipp Hövel, Eckehard Schöll
- Physical review letters
- 2011

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatiotemporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of… (More)

- V Flunkert, S Yanchuk, T Dahms, E Schöll
- Physical review letters
- 2010

Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral properties of the network topology. The master stability function used to determine the stability of synchronous solutions… (More)

- B Hauschildt, N B Janson, A Balanov, E Schöll
- Physical review. E, Statistical, nonlinear, and…
- 2006

We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modeled as FitzHugh-Nagumo systems with parameter values at which no autonomous oscillations occur, and each unit is forced by its own source of random fluctuations. Application of delayed… (More)

- N B Janson, A G Balanov, E Schöll
- Physical review letters
- 2004

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength.… (More)

- Iryna Omelchenko, Bruno Riemenschneider, Philipp Hövel, Yuri Maistrenko, Eckehard Schöll
- Physical review. E, Statistical, nonlinear, and…
- 2012

We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wavelike profiles and study the transition from coherence to incoherence… (More)

We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of… (More)