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- Nilüfer Baba, Katharina Krischer
- Chaos (Woodbury, N.Y.)
- 2008

We studied the dynamics of a prototypical electrochemical model, the electro-oxidation of hydrogen in the presence of poisons, under galvanostatic conditions. The lumped system exhibits relaxation oscillations, which develop mixed-mode oscillations (MMOs) for low preset currents. A fast-slow analysis of the homogeneous dynamics reveals that the MMOs arise… (More)

- Adrian Bîrzu, Katharina Krischer
- Chaos (Woodbury, N.Y.)
- 2010

We investigate the dynamics of a population of globally coupled FitzHugh-Nagumo oscillators with a time-periodic coupling strength. While for synchronizing global coupling, the in-phase state is always stable, the oscillators split into several cluster states for desynchronizing global coupling, most commonly in two, irrespective of the coupling strength.… (More)

- Lennart Schmidt, Katharina Krischer
- Physical review letters
- 2015

The coexistence of coherently and incoherently oscillating parts in a system of identical oscillators with symmetrical coupling, i.e., a chimera state, is even observable with uniform global coupling. We address the question of the prerequisites for these states to occur in globally coupled systems. By analyzing two different types of chimera states found… (More)

- Lennart Schmidt, Katharina Krischer
- Chaos (Woodbury, N.Y.)
- 2015

We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transition towards a related chimera state. We demonstrate that the diffusional coupling is non-essential for these complex… (More)

- Sindre W. Haugland, Lennart Schmidt, Katharina Krischer
- Scientific reports
- 2015

Oscillatory media can exhibit the coexistence of synchronized and desynchronized regions, so-called chimera states, for uniform parameters and symmetrical coupling. In a phase-balanced chimera state, where the totals of synchronized and desynchronized regions, respectively, are of the same size, the symmetry of the system predicts that interchanging both… (More)

- Felix P Kemeth, Sindre W Haugland, Lennart Schmidt, Ioannis G Kevrekidis, Katharina Krischer
- 2016

We present a universal characterization scheme for chimera states applicable to both numerical and experimental data sets. The scheme is based on two correlation measures that enable a meaningful definition of chimera states as well as their classification into three categories: stationary, turbulent and breathing. In addition, these categories can be… (More)

Uncertain recognition success, unfavorable scaling of connection complexity, or dependence on complex external input impair the usefulness of current oscillatory neural networks for pattern recognition or restrict technical realizations to small networks. We propose a network architecture of coupled oscillators for pattern recognition which shows none of… (More)

- Philipp R. Bauer, Antoine Bonnefont, Katharina Krischer
- Scientific reports
- 2015

Collisions of excitation pulses in dissipative systems lead usually to their annihilation. In this paper, we report electrochemical experiments exhibiting more complex pulse interaction with collision survival and pulse splitting, phenomena that have rarely been observed experimentally and are only poorly understood theoretically. Using spatially resolved… (More)

- Lennart Schmidt, Katharina Krischer
- Physical review. E, Statistical, nonlinear, and…
- 2014

We study two-cluster solutions of an ensemble of generic limit-cycle oscillators in the vicinity of a Hopf bifurcation, i.e., Stuart-Landau oscillators, with a nonlinear global coupling. This coupling leads to conserved mean-field oscillations acting back on the individual oscillators as a forcing. A reduction to two effective equations makes a linear… (More)