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Research Papers

Effect of Noise on Generalized Synchronization: An Experimental Perspective

[+] Author and Article Information
Anirban Ray

e-mail: anirban.chaos@gmail.com

A. RoyChowdhury

e-mail: arc.roy@gmail.com

Sankar Basak

e-mail: basak.sankar8@gmail.com
High Energy Physics Division,
Department of Physics,
Jadavpur University,
Kolkata 700032, India

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received November 16, 2011; final manuscript received August 9, 2012; published online October 30, 2012. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 8(3), 031003 (Oct 30, 2012) (7 pages) Paper No: CND-11-1218; doi: 10.1115/1.4007445 History: Received November 16, 2011; Revised August 09, 2012

Generalized synchronization between two different nonlinear systems under influence of noise is studied with the help of an electronic circuit and numerical experiment. In the present case, we have studied the phenomena of generalized synchronization between the Lorenz system and another nonlinear system (modified Lorenz) proposed in Ray et al. (2011, “On the Study of Chaotic Systems With Non-Horseshoe Template,” Frontier in the Study of Chaotic Dynamical Systems With Open Problems, Vol. 16, E. Zeraoulia and J. C. Sprott, eds., World Scientific, Singapore, pp. 85–103) from the perspective of electronic circuits and corresponding data collected digitally. Variations of the synchronization threshold with coupling (between driver and driven system) and noise intensity have been studied in detail. Later, experimental results are also proved numerically. It is shown that in certain cases, noise enhances generalized synchronization, and in another it destroys generalized synchronization. Numerical studies in the latter part have also proved results obtained experimentally.

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References

Figures

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Fig. 1

Circuit diagram of the electronic circuit for generalized synchronization. Here Lorenz is the driver and modified Lorenz is driven.

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Fig. 2

Circuit diagrams. (a) Lorenz system (driver). (b) Modified Lorenz system (driven).

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Fig. 3

Circuit diagrams. (a) Coupling between two circuits. (b) Noise generator circuit.

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Fig. 4

Circuit diagrams. (a) Variation of RMS value of error with coupling c' for different value of noise intensity D. As evident from the figure, as noise increases, synchronization arises for a lot less of a value of c'. (b) Lorenz system (driver) in xz plane. (c) Modified Lorenz system (driven) in xz plane. (d) At synchronized state, phase space between x variable of Lorenz system and modified Lorenz system.

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Fig. 5

Variation of synchronization threshold for different values of coupling strength (c') and noise intensity (D)

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Fig. 6

Circuit diagram of the electronic circuit for generalized synchronization. Here, Lorenz is driven and Modified Lorenz is the driver.

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Fig. 7

Circuit diagrams. (a) Modified Lorenz system (driver). (b) Lorenz system (driven).

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Fig. 8

Variation of RMS value of error with coupling c' for different values of noise intensity D. As evident from the figure, noise destroys synchronization.

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Fig. 9

Variation of synchronization threshold for different values of coupling strength (c') and noise intensity (D)

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Fig. 10

Circuit diagrams. (a) Variation of RMS value of error with coupling c' for different values of noise intensity D. Here, results are obtained numerically. (b) Variation of maximum conditional Lyapunov exponent with coupling (c') for different noise intensity D.

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Fig. 11

Circuit diagrams. (a) Variation of RMS value of error with coupling c' for different values of noise intensity D when Lorenz is the driven system and the modified Lorenz is the driver. (b) Variation of maximum conditional Lyapunov exponent of Lorenz system with coupling (c') for different noise intensity D.

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