69 research outputs found
Generalized synchronization: a modified system approach
The universal mechanism resulting in the generalized synchronization regime
arising in the chaotic oscillators with the dissipative coupling has been
described. The reasons of the generalized synchronization occurrence may be
clarified by means of a modified system approach. The main results are
illustrated by unidirectionally coupled Rossler systems, Rossler and Lorenz
systems and logistic maps.Comment: 4 pages, 2 figure
An Analysis of Design Problems in Combinatorial Procurement Auctions
Traditional auction mechanisms support price negotiations on a single item. The Internet allows for the exchange of much more complex offers in real-time. This is one of the reasons for much research on multidimensional auction mechanisms allowing negotiations on multiple items, multiple units, or multiple attributes of an item, as they can be regularly found in procurement. Combinatorial auctions, for example, enable suppliers to submit bids on bundles of items. A number of laboratory experiments has shown high allocative efficiency in markets with economies of scope. For suppliers it is easier to express cost savings due to bundling (e. g., decreased transportation or production costs). This can lead to significant savings in total cost of the procurement manager. Procurement negotiations exhibit a number of particularities: â It is often necessary to consider qualitative attributes or volume discounts in bundle bids. These complex bid types have not been sufficiently analyzed. â The winner determination problem requires the consideration of a number of additional business constraints, such as limits on the spend on a particular supplier or the number of suppliers. â Iterative combinatorial auctions have a number of advantages in practical applications, but they also lead to new problems in the determination of ask prices. In this paper, we will discuss fundamental problems in the design of combinatorial auctions and the particularities of procurement applications. Reprint of an article from WIRTSCHAFTSINFORMATIK 47(2)2005:126â134
Time scale synchronization of chaotic oscillators
This paper presents the result of the investigation of chaotic oscillator
synchronization. A new approach for detecting of synchronized behaviour of
chaotic oscillators has been proposed. This approach is based on the analysis
of different time scales in the time series generated by the coupled chaotic
oscillators. This approach has been applied for the coupled Rossler and Lorenz
systems.Comment: 19 pages, 12 figure
Detecting synchronization of self-sustained oscillators by external driving with varying frequency
We propose a method for detecting the presence of synchronization of
self-sustained oscillator by external driving with linearly varying frequency.
The method is based on a continuous wavelet transform of the signals of
self-sustained oscillator and external force and allows one to distinguish the
case of true synchronization from the case of spurious synchronization caused
by linear mixing of the signals. We apply the method to driven van der Pol
oscillator and to experimental data of human heart rate variability and
respiration.Comment: 9 pages, 7 figure
Detection of synchronization from univariate data using wavelet transform
A method is proposed for detecting from univariate data the presence of
synchronization of a self-sustained oscillator by external driving with varying
frequency. The method is based on the analysis of difference between the
oscillator instantaneous phases calculated using continuous wavelet transform
at time moments shifted by a certain constant value relative to each other. We
apply our method to a driven asymmetric van der Pol oscillator, experimental
data from a driven electronic oscillator with delayed feedback and human
heartbeat time series. In the latest case, the analysis of the heart rate
variability data reveals synchronous regimes between the respiration and slow
oscillations in blood pressure.Comment: 10 pages, 9 figure
Infinities of stable periodic orbits in systems of coupled oscillators
We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor
Synchronization of Coupled Systems with Spatiotemporal Chaos
We argue that the synchronization transition of stochastically coupled
cellular automata, discovered recently by L.G. Morelli {\it et al.} (Phys. Rev.
{\bf 58 E}, R8 (1998)), is generically in the directed percolation universality
class. In particular, this holds numerically for the specific example studied
by these authors, in contrast to their claim. For real-valued systems with
spatiotemporal chaos such as coupled map lattices, we claim that the
synchronization transition is generically in the universality class of the
Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.Comment: 4 pages, including 3 figures; submitted to Phys. Rev.
Strong Effects of Network Architecture in the Entrainment of Coupled Oscillator Systems
Entrainment of randomly coupled oscillator networks by periodic external
forcing applied to a subset of elements is numerically and analytically
investigated. For a large class of interaction functions, we find that the
entrainment window with a tongue shape becomes exponentially narrow for
networks with higher hierarchical organization. However, the entrainment is
significantly facilitated if the networks are directionally biased, i.e.,
closer to the feedforward networks. Furthermore, we show that the networks with
high entrainment ability can be constructed by evolutionary optimization
processes. The neural network structure of the master clock of the circadian
rhythm in mammals is discussed from the viewpoint of our results.Comment: 15 pages, 11 figures, RevTe
Chaotic Observer-based Synchronization Under Information Constraints
Limit possibilities of observer-based synchronization systems under
information constraints (limited information capacity of the coupling channel)
are evaluated. We give theoretical analysis for multi-dimensional
drive-response systems represented in the Lurie form (linear part plus
nonlinearity depending only on measurable outputs). It is shown that the upper
bound of the limit synchronization error (LSE) is proportional to the upper
bound of the transmission error. As a consequence, the upper and lower bounds
of LSE are proportional to the maximum rate of the coupling signal and
inversely proportional to the information transmission rate (channel capacity).
Optimality of the binary coding for coders with one-step memory is established.
The results are applied to synchronization of two chaotic Chua systems coupled
via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference
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