267 research outputs found
Floquet Stability Analysis of Ott-Grebogi-Yorke and Difference Control
Stabilization of instable periodic orbits of nonlinear dynamical systems has
been a widely explored field theoretically and in applications. The techniques
can be grouped in time-continuous control schemes based on Pyragas, and the two
Poincar\'e-based chaos control schemes, Ott-Gebogi-Yorke (OGY) and difference
control. Here a new stability analysis of these two Poincar\'e-based chaos
control schemes is given by means of Floquet theory. This approach allows to
calculate exactly the stability restrictions occuring for small measurement
delays and for an impulse length shorter than the length of the orbit. This is
of practical experimental relevance; to avoid a selection of the relative
impulse length by trial and error, it is advised to investigate whether the
used control scheme itself shows systematic limitations on the choice of the
impulse length. To investigate this point, a Floquet analysis is performed. For
OGY control the influence of the impulse length is marginal. As an unexpected
result, difference control fails when the impulse length is taken longer than a
maximal value that is approximately one half of the orbit length for small
Ljapunov numbers and decreases with the Ljapunov number.Comment: 13 pages. To appear in New Journal of Physic
Switching between periodic orbits in impact oscillator by time-delayed feedback methods
Acknowledgements The authors also acknowledge the financial support from Coordenação de Aperfeiçoamento do Pessoal de Nivel Superior (CAPES), under the Grant Number 88881.189487/2018-01 and FAPERJ.Peer reviewedPublisher PD
Strange Nonchaotic Attractors In A Periodically Forced Piecewise Linear System With Noise
Acknowledgments This work is supported by the National Natural Science Foundation of China (NNSFC) (Nos. 12072291, 11732014 and 12172306)Peer reviewedPostprin
Calculation of nonlinear vibrations of piecewise-linear systems using the shooting method
In this paper, an explicit formulation of the shooting scheme for computation of multiple periodic attractors of a harmonically excited oscillator which is asymmetric with both stiffness and viscous damping piecewise linearities is derived. The numerical simulation by the shooting method is compared with that by the incremental harmonic balance method (IHB method), which shows that the shooting method is in many respects distinctively advantageous over the incremental harmonic balance method
On the stability of periodic orbits in delay equations with large delay
We prove a necessary and sufficient criterion for the exponential stability
of periodic solutions of delay differential equations with large delay. We show
that for sufficiently large delay the Floquet spectrum near criticality is
characterized by a set of curves, which we call asymptotic continuous spectrum,
that is independent on the delay.Comment: postprint versio
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