- August 2019 - Lyapunov spectra and collective modes of chimera states in globally coupled Stuart-Landau oscillators
Oscillatory systems with long-range or global coupling offer promising insight into the interplay between high-dimensional (or microscopic) chaotic motion and collective interaction patterns. Within this paper, we use Lyapunov analysis to investigate whether chimera states in globally coupled Stuart-Landau (SL) oscillators exhibit collective degrees of freedom. We compare two types of chimera states, which emerge in SL ensembles with linear and nonlinear global coupling, respectively, the latter introducing a constraint that conserves the oscillation of the mean. Lyapunov spectra reveal that for both chimera states the Lyapunov exponents split into several groups with different convergence properties in the limit of large system size. Furthermore, in both cases the Lyapunov dimension is found to scale extensively and the localization properties of covariant Lypunov vectors manifest the presence of collective Lyapunov modes. Here, however, we find qualitative differences between the two types of chimera states: Whereas the ones in the system under nonlinear global coupling exhibit only slow collective modes corresponding to Lyapunov exponents equal or close to zero, those which experience the linear mean-field coupling exhibit also faster collective modes associated with Lyapunov exponents with large positive or negative values. Furthermore, for the fastest collective mode we showed that it spreads across both synchonous and incoherent oscillators.
- August 2019 - 70th Annual Meeting of the International Society of Electrochemistry
We are happy to announce that the price for best poster at this years annual meeting of the ISE was awarded to our own Thomas L. Maier. Maiers outstanding poster was choosen as one of the best ones out of the approximately 300 that were presented.
- April 2019 - Bichaoticity Induced by Inherent Birhythmicity During the Oscillatory Electrodissolution of Silicon
The electrodissolution of p-type silicon in a fluoride-containing electrolyte is a prominent electrochemical oscillator with a still unknown oscillation mechanism. In this article, we present a study of its dynamical states occurring in a wide range of the applied voltage–external resistance parameter plane. We provide evidence that the system possesses inherent birhythmicity, and thus at least two distinct feedback loops promoting oscillatory behavior. The two parameter regions in which the different limit cycles exist are separated by a band in which the dynamics exhibit bistability between two branches with different multimode oscillations. Following the states along one path through this bistable region, one observes that each branch undergoes a different transition to chaos, namely, a period doubling cascade and a quasiperiodic route with a torus-breakdown, respectively, making Si electrodissolution one of the few experimental systems exhibiting bichaoticity.
For the full article postprint, see here.
- February 2019 - A Physical Model for the Regime of Negative Dierential Resistance
When Si is anodically oxidized in a fluoride containing electrolyte, an oxide layer is grown. Simultaneously, the layer is etched by the fluoride containing electrolyte. The resulting stationary state exhibits a negative slope of the current-voltage characteristics in a certain range of applied voltage. We propose a physical model that reproduces this negative slope. In particular, our model assumes that the oxide layer consists of both partially and fully oxidized Si and that the etch rate depends on the effective degree of oxidation. Finally, we show that our simulations are in good agreement with measurements of the current-voltage characteristics, the oxide layer thickness, the dissolution valence, and the impedance spectra of the electrochemical system.
For the full article postprint, see here.
- February 2019 - Cluster singularity
Certain swarms of fireflies are known to flash in unison. They also sometimes divide into two or more distinct yet internally synchronized groups, flashing with a certain phase lag between the groups. This is just one example of clustering dynamics in an ensemble of coupled oscillators, as it occurs naturally in many physical systems. A key problem in the understanding of clustering dynamics is the connection between its occurrence in small and large ensembles. In other words, is there a universal law governing the arrangement of cluster states, independent of the system size? This paper partially answers this question and links the phenomenon of clustering in minimal networks of globally coupled limit-cycle oscillators to clustering in ensembles of infinitely many oscillators. We demonstrate that a natural arrangement of such 2-cluster states exists: When tuning a parameter, a balanced cluster state transitions to synchronized motion via a sequence of intermediate unbalanced cluster states. Tuning an additional parameter, this sequence converges to a single point in parameter space where all cluster states are born directly at the synchronized solution. We call such a codimension-2 point a cluster singularity. Singularities of this kind may appear in any symmetrically coupled ensemble of oscillators and thus play a crucial role for the understanding of collective behavior in oscillatory systems.
For the full article, see here.
- April 26th 2018 - The different faces of chimera states
Oscillatory networks play a crucial role in the understanding of complex systems such as the brain or electric power grids. Such networks may exhibit a vast variety of different dynamical phenomena, the underlying mechanisms of which still raise many questions. These phenomena include so-called chimera states, extraordinary chaotic states in which some of the oscillators show synchronized motion, whereas some others behave incoherently. Even these states might occur in different variations on which we shed some light in this letter. Starting from very small networks of just four oscillators, we show that one can distinguish such chimera states using symmetry arguments: Some chimeras behave in a way which leaves the dynamical structure unchanged when some of the oscillators are interchanged, whereas other chimera states do not have that particular invariance. This difference in the symmetry properties may also be used to distinguish between states in larger ensembles of coupled oscillators. Our results might help elucidating dynamics of partial synchrony occurring in nature, for example during unihemispheric sleep in certain animals.
For the full article preprint, see here.
- November 2nd 2016
Python code for the classification of chimera states is now available, and can be installed using (sudo) pip install classify_chimeras or from source via the GitHub repository.
For further reading, see A classification scheme for chimera states.
- November 2nd 2016
New group picture now online here