7,522 research outputs found
Amplitude Death: The emergence of stationarity in coupled nonlinear systems
When nonlinear dynamical systems are coupled, depending on the intrinsic
dynamics and the manner in which the coupling is organized, a host of novel
phenomena can arise. In this context, an important emergent phenomenon is the
complete suppression of oscillations, formally termed amplitude death (AD).
Oscillations of the entire system cease as a consequence of the interaction,
leading to stationary behavior. The fixed points that the coupling stabilizes
can be the otherwise unstable fixed points of the uncoupled system or can
correspond to novel stationary points. Such behaviour is of relevance in areas
ranging from laser physics to the dynamics of biological systems. In this
review we discuss the characteristics of the different coupling strategies and
scenarios that lead to AD in a variety of different situations, and draw
attention to several open issues and challenging problems for further study.Comment: Physics Reports (2012
Reconstructing phase dynamics of oscillator networks
We generalize our recent approach to reconstruction of phase dynamics of
coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205
(2008)] to cover the case of small networks of coupled periodic units. Starting
from the multivariate time series, we first reconstruct genuine phases and then
obtain the coupling functions in terms of these phases. The partial norms of
these coupling functions quantify directed coupling between oscillators. We
illustrate the method by different network motifs for three coupled oscillators
and for random networks of five and nine units. We also discuss nonlinear
effects in coupling.Comment: 6 pages, 5 figures, 27 reference
Enhancing synchronization in chaotic oscillators by induced heterogeneity
We report enhancing of complete synchronization in identical chaotic
oscillators when their interaction is mediated by a mismatched oscillator. The
identical oscillators now interact indirectly through the intermediate relay
oscillator. The induced heterogeneity in the intermediate oscillator plays a
constructive role in reducing the critical coupling for a transition to
complete synchronization. A common lag synchronization emerges between the
mismatched relay oscillator and its neighboring identical oscillators that
leads to this enhancing effect. We present examples of one-dimensional open
array, a ring, a star network and a two-dimensional lattice of dynamical
systems to demonstrate how this enhancing effect occurs. The paradigmatic
R\"ossler oscillator is used as a dynamical unit, in our numerical experiment,
for different networks to reveal the enhancing phenomenon.Comment: 10 pages, 7 figure
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