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Keywords
(8)
Chaotic Dynamics
Chaotic System
Control Theory
Dynamic System
Invariant Manifold
Linear Stability
Mutual Coupling
Satisfiability
Related Publications
(1)
Intermittent Loss of Synchronization in Coupled Chaotic Oscillators: Toward a New Criterion for HighQuality Synchronization
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Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds
Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds,10.1063/1.166213,Chaos,Reggie Brown,Nikolai F. Rulkov
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Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds
(
Citations: 23
)
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Reggie Brown
,
Nikolai F. Rulkov
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to perturbations. An easy to use approximate criterion for estimating
linear stability
is also presented. One major advantage of these criteria is that, for simple systems, many of the calculations needed to implement them can be performed analytically. Geometrical interpretations of the criterion are discussed, as well as how they may be used to investigate synchronization between mutual coupled systems and the stability of invariant manifolds within a dynamical system. Finally, the relationship between our criterion and results from
control theory
are discussed. Analytical and numerical results from tests of these criteria on four different dynamical systems are presented.
Journal:
Chaos
, vol. 7, pp. 395413, 1997
DOI:
10.1063/1.166213
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Citation Context
(7)
...Although there exist criteria that guarantee highquality synchronization [26, 29,
30
], these are often either to dicult to apply or too conservative [31]...
Lucas Illing
.
Digital communication using chaos and nonlinear dynamics
...According to the chaotic synchronization theory, if the coupling coefficient is selected appropriately, for large values of , the estimated and the actual trajectory will be very close to each other [
24
]...
Ajeesh P. Kurian
,
et al.
Weak Signal Estimation in Chaotic Clutter Using ModelBased Coupled Sy...
...In the combined state space of such systems, an invariant manifold consisting of the synchronized states, termed generalized synchronization manifold ,i s ac entral object of study in this context, and its form [12] and stability [
9
, 16] are two of its important properties...
Jie Sun
,
et al.
Constructing Generalized Synchronization Manifolds by Manifold Equatio...
...The Jacobean matrix for the above system is given by [
23
]...
...The eigen values λ for the above mentioned Jacobean matrix are given by [
23
]...
...We looked at the natural measures on the chaotic attractor [
23
]...
...The dynamics of the Lorenz system has a chaotic attractor for σ =1 0 ,β = 8/ 3a ndρ = 60. The numerically calculated [
23
] values of <x 1 >, < x2 >a nd < x3 > are 0, 0, 54.81 respectively...
G. K. Patra
,
et al.
Secure Chaotic Synchronization Using Negative Feedback of SuperPositi...
...Due to the similarity between the coupled synchronization and the nonlinear observer design problem, there has been a great deal of interest in applying methods from control theory for chaotic synchronization [
6
]–[13]...
...In [
6
], it is demonstrated that intervals of desynchronization bursting behavior can appear in coupled synchronization when noise is present in the system...
Ajeesh P. Kurian
,
et al.
Performance Analysis of NonlinearPredictiveFilterBased Chaotic Sync...
References
(4)
Synchronization of Chaotic Systems
(
Citations: 6
)
U. Feldmann
Published in 1995.
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(
Citations: 10
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Eduardo D. Sontag
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Citations
(23)
The Impact of the 80Hour Work Week on Student Interest in a Surgical Career 1
Barbara Zarebczan
,
Victoria Rajamanickam
,
Barbara Lewis
,
Glen Leverson
,
Rebecca S. Sippel
Journal:
Journal of Surgical Research  J SURG RES
, vol. 171, no. 2, pp. 422426, 2011
Synchronization of coupled limit cycles
(
Citations: 1
)
Georgi S. Medvedev
Published in 2010.
A new Lyapunov approach for global synchronization of nonautonomous chaotic systems
Xiaofeng Wu
,
Zhifang Gui
,
Qian Lin
,
Jianping Cai
Journal:
Nonlinear Dynamics
, vol. 59, no. 3, pp. 427432, 2010
Digital communication using chaos and nonlinear dynamics
(
Citations: 6
)
Lucas Illing
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 71, no. 12, pp. e2958e2964, 2009
Weak Signal Estimation in Chaotic Clutter Using ModelBased Coupled Synchronization
(
Citations: 2
)
Ajeesh P. Kurian
,
Henry Leung
Journal:
IEEE Transactions on Circuits and Systems Iregular Papers  IEEE TRANS CIRCUIT SYSTI
, vol. 56, no. 4, pp. 820828, 2009