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by Keyword: Oscillators


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Ruzzene, G., Omelchenko, I., Schöl, E., Zakharova, A., Andrzejak, R. G. , (2019). Controlling chimera states via minimal coupling modification Chaos: An Interdisciplinary Journal of Nonlinear Science 29, (5), 051103

We propose a method to control chimera states in a ring-shaped network of nonlocally coupled phase oscillators. This method acts exclusively on the network’s connectivity. Using the idea of a pacemaker oscillator, we investigate which is the minimal action needed to control chimeras. We implement the pacemaker choosing one oscillator and making its links unidirectional. Our results show that a pacemaker induces chimeras for parameters and initial conditions for which they do not form spontaneously. Furthermore, the pacemaker attracts the incoherent part of the chimera state, thus controlling its position. Beyond that, we find that these control effects can be achieved with modifications of the network’s connectivity that are less invasive than a pacemaker, namely, the minimal action of just modifying the strength of one connection allows one to control chimeras.

Keywords: Complex networks, Oscillators, Spatiotemporal phenomena


Andrzejak, R. G. , Ruzzene, G., Malvestio, I., Schindler, K., Schöl, E., Zakharova, A., (2018). Mean field phase synchronization between chimera states Chaos: An Interdisciplinary Journal of Nonlinear Science 28, (9), 091101

We study two-layer networks of identical phase oscillators. Each individual layer is a ring network for which a non-local intra-layer coupling leads to the formation of a chimera state. The number of oscillators and their natural frequencies is in general different across the layers. We couple the phases of individual oscillators in one layer to the phase of the mean field of the other layer. This coupling from the mean field to individual oscillators is done in both directions. For a sufficient strength of this interlayer coupling, the phases of the mean fields lock across the two layers. In contrast, both layers continue to exhibit chimera states with no locking between the phases of individual oscillators across layers, and the two mean field amplitudes remain uncorrelated. Hence, the networks’ mean fields show phase synchronization which is analogous to the one between low-dimensional chaotic oscillators. The required coupling strength to achieve this mean field phase synchronization increases with the mismatches in the network sizes and the oscillators’ natural frequencies.

Keywords: Chaos, Complex networks, Oscillators, Synchronisation


Andrzejak, Ralph G., Ruzzene, G., Malvestio, I., (2017). Generalized synchronization between chimera states Chaos: An Interdisciplinary Journal of Nonlinear Science 27, (5), 053114

Networks of coupled oscillators in chimera states are characterized by an intriguing interplay of synchronous and asynchronous motion. While chimera states were initially discovered in mathematical model systems, there is growing experimental and conceptual evidence that they manifest themselves also in natural and man-made networks. In real-world systems, however, synchronization and desynchronization are not only important within individual networks but also across different interacting networks. It is therefore essential to investigate if chimera states can be synchronized across networks. To address this open problem, we use the classical setting of ring networks of non-locally coupled identical phase oscillators. We apply diffusive drive-response couplings between pairs of such networks that individually show chimera states when there is no coupling between them. The drive and response networks are either identical or they differ by a variable mismatch in their phase lag parameters. In both cases, already for weak couplings, the coherent domain of the response network aligns its position to the one of the driver networks. For identical networks, a sufficiently strong coupling leads to identical synchronization between the drive and response. For non-identical networks, we use the auxiliary system approach to demonstrate that generalized synchronization is established instead. In this case, the response network continues to show a chimera dynamics which however remains distinct from the one of the driver. Hence, segregated synchronized and desynchronized domains in individual networks congregate in generalized synchronization across networks.

Keywords: Oscillators, Synchronisation


Schulz, S., Legorburu Cladera, B., Giraldo, B., Bolz, M., Bar, K. J., Voss, A., (2017). Neuronal desynchronization as marker of an impaired brain network Engineering in Medicine and Biology Society (EMBC) 39th Annual International Conference of the IEEE , IEEE (Seogwipo, South Korea) , 2251-2254

Synchronization is a central key feature of neural information processing and communication between different brain areas. Disturbance of oscillatory brain rhythms and decreased synchronization have been associated with different disorders including schizophrenia. The aim of this study was to investigate whether synchronization (in relaxed conditions with no stimuli) between different brain areas within the delta, theta, alpha (alpha1, alpha2), beta (beta1, beta2), and gamma bands is altered in patients with a neurological disorder in order to generate significant cortical enhancements. To achieve this, we investigated schizophrenic patients (SZO; N=17, 37.5±10.4 years, 15 males) and compared them to healthy subjects (CON; N=21, 36.7±13.4 years, 15 males) applying the phase locking value (PLV). We found significant differences between SZO and CON in different brain areas of the theta, alpha1, beta2 and gamma bands. These areas are related to the central and parietal lobes for the theta band, the parietal lobe for the alpha1, the parietal and frontal for the beta2 and the frontal-central for the gamma band. The gamma band revealed the most significant differences between CON and SZO. PLV were 61.7% higher on average in SZO in most of the clusters when compared to CON. The related brain areas are directly related to cognition skills which are proved to be impaired in SZO. The results of this study suggest that synchronization in SZO is also altered when the patients were not asked to perform a task that requires their cognitive skills (i.e., no stimuli are applied - in contrast to other findings).

Keywords: Synchronization, Electroencephalography, Electrodes, Brain, Time series analysis, Oscillators, Frequency synchronization