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- CHRISTIAN BICK
- 2009

The Lotka-Volterra equations can be used to model the behavior of complex systems in nature. Trajectories in a stable heteroclinic channel describe transient dynamics according to the winnerless competition principle in such a system. The existence of such a channel is guaranteed if the parameters of the Lotka-Volterra equations satisfy a number of… (More)

- Christian Bick, Marc Timme, Danilo Paulikat, Dirk Rathlev, Peter Ashwin
- Physical review letters
- 2011

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic… (More)

- Christian Bick, Peter Ashwin, Ana Rodrigues
- Chaos
- 2016

The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony… (More)

- Christian Bick, Marc Timme, Christoph Kolodziejski
- SIAM J. Applied Dynamical Systems
- 2012

Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed is of crucial importance. Here we present a predictive feedback chaos control method that adapts a control parameter… (More)

Since chaos control has found its way into many applications, the development of fast, easy-to-implement and universally applicable chaos control methods is of crucial importance. Predictive feedback control has been widely applied but suffers from a speed limit imposed by highly unstable periodic orbits. We show that this limit can be overcome by stalling… (More)

- Erik A Martens, Christian Bick, Mark J Panaggio
- Chaos
- 2016

The simplest network of coupled phase-oscillators exhibiting chimera states is given by two populations with disparate intra- and inter-population coupling strengths. We explore the effects of heterogeneous coupling phase-lags between the two populations. Such heterogeneity arises naturally in various settings, for example, as an approximation to… (More)

- Peter Ashwin, Christian Bick, Oleksandr Burylko
- Front. Appl. Math. Stat.
- 2016

For a system of coupled identical phase oscillators with full permutation symmetry, any broken symmetries in dynamical behavior must come from spontaneous symmetry breaking, i.e., from the nonlinear dynamics of the system. The dynamics of phase differences for such a system depends only on the coupling (phase interaction) function g(φ) and the number of… (More)

- Christian Bick, Christoph Kolodziejski, Marc Timme
- Chaos
- 2014

Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize… (More)

- Christian Bick
- J. Nonlinear Science
- 2017

The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector-for coupled phase oscillators the… (More)

Academic Interests Group theory and combinatorics (in particular groups acting on rooted trees, growth of groups, regular combings of groups, random walks on groups, and dynamical systems) Dynamical Systems (in particuliar iteration of holomorphic maps). Computer algebra and computational group theory

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