Master-slave synchronization and the Lorenz equations.

@article{Balmforth1997MasterslaveSA,
  title={Master-slave synchronization and the Lorenz equations.},
  author={Neil J. Balmforth and Charles Philippe Tresser and Patrick A. Worfolk and Chai Wah Wu},
  journal={Chaos},
  year={1997},
  volume={7 3},
  pages={
          392-394
        }
}
Since the seminal remark by Pecora and Carroll [Phys. Rev. Lett. 64, 821 (1990)] that one can synchronize chaotic systems, the main example in the related literature has been the Lorenz equations. Yet this literature contains a mixture of true and false, and of justified and unsubstantiated claims about the synchronization properties of the Lorenz equations. In this note we clarify some of the confusion. (c) 1997 American Institute of Physics. 
View on PubMed
math.ubc.ca
25 Citations
Highly Influential Citations
1
Background Citations
4
Methods Citations
1

25 Citations

Citation Type

Citation Type

On the geometry of master-slave synchronization.
TLDR
The results are variations on the theme that projection often can compensate for expansion, which are all inspired by a similar geometric and coordinate independent point of view to the one introduced in master-slave synchronization by Tresser, Worfolk, and Bass.
Projective Synchronization In Three-Dimensional Chaotic Systems
TLDR
It is shown that, for the nonsynchronizing variable, synchronization up to a scale factor is possible, and the mechanism for this projective form of chaotic synchronization in three-dimensional systems is explained.
The synchronization of chaotic systems
Stages of chaotic synchronization.
TLDR
It is found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems.
Indirect master-slave synchronization: experimental results
Adaptive Observers With Persistency of Excitation for Synchronization of Chaotic Systems
TLDR
This work addresses the problem of master-slave synchronization of chaotic systems under parameter uncertainty and with partial measurements and shows that synchronization is achievable in a practical sense, that is, with ¿small¿ error.
The Synchronized Dynamics of Complex Systems
A stochastic model of synchronization for chaotic pendulums
A note on the synchronization for a class of possible nonsmooth discrete chaotic systems
In this paper, synchronization for n-dimensional discrete systems is analyzed and a general framework is proposed. It is considered synchronization for nonsmooth discrete systems in the form of a…
Synchronizing strict-feedback chaotic system via a scalar driving signal.
We propose a systematic design procedure to synchronize a class of chaotic system in a so-called strict-feedback form based on back-stepping procedure. This approach needs only a scalar driving…
...
1
2
3
...

References

SHOWING 1-10 OF 10 REFERENCES
Master-slave synchronization from the point of view of global dynamics.
TLDR
This work presents a mathematical framework for the theory of a synchronization phenomenon for dynamical systems discovered by Pecora and Carroll and uses its insights to synchronize nonlinear systems which were not previously recognized as being synchronizable.
Analysis and synthesis of synchronous periodic and chaotic systems.
  • He, Vaidya
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
TLDR
A necessary and sufficient condition for synchronization is presented and has been used to create a high-dimensional chaotic system with a nonlinear subsystem that shows synchronization both when it exhibits periodic limit cycles and when it turns chaotic.
Driving systems with chaotic signals.
TLDR
Numerical simulations show that the negativity of the conditional Lyapunov exponents does not always guarantee synchronization and, additionally, the domain of initial conditions for the drive variables needs to be specified in which case the synchronization occurs.
A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS
TLDR
A framework for synchronization of dynamical systems which unifies many results in synchronization and control of Dynamical systems, in particular chaotic systems is given and the main tool to prove asymptotical stability and synchronization is Lyapunov stability theory.
A wait-and-reset strategy to synchronizing chaotic systems
Synchronization of chaotic orbits: The effect of a finite time step.
  • Amritkar, Gupte
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1993
TLDR
The synchronization criterion reduces to the usual subsystem-Lyapunov-exponent criterion in the limit of the time step tending to zero and it is found that a procedure where the drive variable is set at discrete times can also achieve synchronization.
Circuit implementation of synchronized chaos with applications to communications.
Deterministic nonperiodic flow
Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with…
Deterministic non-periodic ow
  • J. Atmos. Sci
  • 1963
GB. etznjb@thmech.nottingham.ac.uk Charles Tresser: IBM, PO Box 218, Yorktown Heights, NY 10598,USA. tresser@watson.ibm.com Patrick Worfolk: The Geometry Center, 1300 South Second Street
  • GB. etznjb@thmech.nottingham.ac.uk Charles Tresser: IBM, PO Box 218, Yorktown Heights, NY 10598,USA. tresser@watson.ibm.com Patrick Worfolk: The Geometry Center, 1300 South Second Street