Controlling stability of dynamical systems is one of the most important challenges in science and engineering. Hence, there appears to be continuous need to study and develop numerical algorithms of control methods. One of the most frequently applied invariants characterizing systems' stability are Lyapunov exponents (LE).
View Article and Find Full Text PDFThe availability of macroscopic, nearly periodic structures known as eutectics opens a new path for controlling light at wavelength scales determined by the geometrical parameters of these materials and the intrinsic properties of their component phases. Here, we analyze the optical waveguiding properties of eutectic mixtures of alkali halides, formed by close-packed arrangements of aligned cylindrical inclusions. The wavelengths of phonon polaritons in these constituents are conveniently situated in the infrared and are slightly larger than the diameter and separation of the inclusions, typically consisting on single-crystal wires down to submicrometer diameter.
View Article and Find Full Text PDFWe consider the synchronization of two clocks which are accurate (show the same time) but have pendulums with different masses. We show that such clocks hanging on the same beam beside the complete (in-phase) and antiphase synchronizations perform the third type of synchronization in which the difference of the pendulums' displacements is a periodic function of time. We identify this period to be a few times larger than the period of pendulums' oscillations in the case when the beam is at rest.
View Article and Find Full Text PDFThis paper is focused on the problem of complete synchronization in arrays of externally driven identical or slightly different oscillators. These oscillators are coupled by common driving which makes an occurrence of generalized synchronization between a driving signal and response oscillators possible. Therefore, the phenomenon of generalized synchronization is also analyzed here.
View Article and Find Full Text PDFPhilos Trans A Math Phys Eng Sci
March 2008
In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
January 2007
We discuss synchronization thresholds in an array of nondiagonally coupled oscillators. We argue that nondiagonal coupling can cause the appearance or disappearance of desynchronous windows in the coupling parameter space. Such a phenomenon is independent of the motion character (periodic or chaotic) of the isolated node system.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
January 2006
We consider the dynamics of a linear array of coupled semiconductor lasers. Particular attention is paid to the synchronous states, which are caused by the permutation of two outer lasers. A system of three coupled lasers is studied in more details.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
August 2004
In this paper, we define a simple criterion of the synchronization threshold in the set of coupled chaotic systems (flows or maps) with diagonal diffusive coupling. The condition of chaotic synchronization is determined only by two "parameters of order," i.e.
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