Eckehard Schöll

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We show that time-delayed feedback methods, which have successfully been used to control unstable periodic orbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the Lambert function and discuss effects of both a low-pass filter included in the control loop and nonzero latency times(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)
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)
Control of spatio-temporal chaos by the time-delay autosynchronization method is improved by several orders of magnitude. Unstable time periodic patterns are efficiently stabilized if one employs filters and couplings which originate from the Floquet eigenvalue problem of the unstable orbit. We illustrate our scheme by an application to a globally coupled(More)
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)
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)
We study the kinetics of growing cell populations by means of a kinetic Monte Carlo method. By applying the same growth mechanism to a two-dimensional (2D) and a three-dimensional (3D) model, and making direct comparison with experimental studies, we show that both models exhibit similar behavior. Based on this we propose a method for establishment of a(More)
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 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 analyzing the eigenvalue(More)
The brain may be conceived as a dynamic network of coupled neurons [1, 2, 3]. These neurons are excitable units which can emit spikes or bursts of electrical signals. In order to describe the complicated interaction between billions of neurons in large neural networks, the neurons are often lumped into highly connected sub-networks or synchronized(More)