An Analytical Study on the Synchronization of Murali—Lakshmanan—Chua Circuits

Sivaganesh, G.

doi:10.1088/0256-307x/32/1/010503

Cited by 13 publications

(16 citation statements)

References 21 publications

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“…The piecewise-linear nature of the nonlinear elements present in these simple systems makes their dynamics to be mathematically tractable. The dynamical process of chaos synchronization observed in unidirectionally and mutually coupled simple chaotic systems have been greatly studied through explicit analytical solutions, numerical simulations and confirmed experimentally [25][26][27][28]. A mathematical analysis based on the time series of the state variables has been presented for the synchronization and signal transmission using chaos in the quadratic and Ueda systems [29].…”

Section: Introductionmentioning

confidence: 95%

“…Now, we find the solution of the state variables x * (t), y * (t) in the regions D * 0 and D * ±1 of the difference system. Analytical solutions of this kind has been studied recently for synchronization in a number of systems [25][26][27][28]. Hence, we summarize the solution for the state equations of the difference system as follows.…”

Section: Explicit Analytical Solutionsmentioning

confidence: 99%

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Generalized analytical solutions for secure transmission of signals using a simple communication scheme with numerical and experimental confirmation

Sivaganesh

Arulgnanam

Seethalakshmi

2019

Chinese Journal of Physics

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A novel explicit analytical solution is reported for the transmission and recovery of information signals using a simple communication scheme. Analytical solutions are obtained for the normalized state equations of coupled second-order chaotic transmitter and receiver systems embedding the information signal. The analytical solution of the difference system obtained from the state equations of the transmitter and receiver systems has been identified as a measure of the recovered information signal which is transmitted securely by chaotic masking. The analytical solutions are used to reveal the nature of synchronization and the enhancement of the amplitude of recovered information signal. The difference signal of the coupled state variables indicating the recovered information signal obtained through numerical simulations is presented to validate the analytical results. The electronic circuit experimental results are presented to confirm the analytical and numerical results of the communication scheme discussed.

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Section: Introductionmentioning

confidence: 95%

Section: Explicit Analytical Solutionsmentioning

confidence: 99%

Generalized analytical solutions for secure transmission of signals using a simple communication scheme with numerical and experimental confirmation

Sivaganesh

Arulgnanam

Seethalakshmi

2019

Chinese Journal of Physics

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“…The chaotic and synchronization dynamics of the circuit has been completely studied experimentally, numerically and analytically [16][17][18][19] . This system exhibits a double-band chaotic attractor at the amplitude of the external force f 1,2 = 0.14.…”

Section: A Murali-lakshmanan-chua Circuitmentioning

confidence: 99%

Stability enhancement by induced synchronization using transient uncoupling in certain coupled chaotic systems

Sivaganesh

Arulgnanam²,

Seethalakshmi

2019

Chaos, Solitons & Fractals

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In this paper, we report the enhanced stability of induced synchronization by transient uncoupling observed in certain unidirectionally coupled second-order chaotic systems. The stability of synchronization observed in the coupled systems subjected to transient uncoupling is analyzed using the Master Stability Function. The existence of the coupled systems in stable synchronized states over a certain range of the clipping fraction of the driven system is identified. The enhanced stable synchronized states are obtained for fixed values of clipping fraction in certain second-order chaotic systems. The two-parameter bifurcation diagram indicating the parameter regions over which stable synchronization occurs is presented. The negative eigenvalue regions of the driven system enabling induced synchronization is studied for all the systems. The enhancement of synchronization through transient uncoupling observed in coupled second-order non-autonomous chaotic systems is reported in the literature for the first time.

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“…From the results of y * (t), x * (t) obtained from Eqs. (18), (21) and y(t), x(t) obtained from Eqs. (5), (6), x ′ (t) and y ′ (t) can be obtained from Eqs.…”

Section: Analytical Solution For Synchronization Of Snasmentioning

confidence: 99%

“…The MSFs for a few nonlinear systems and simple electronic circuits have been studied [19,20]. An explicit analytical solution explaining the complete synchronization of identical Murali−Lakshmanan−Chua circuits has been presented [21,22]. Synchronization of coupled driven-damped SQUIDS exhibiting SNAs in their dynamics have been synchronized using in-phase driving method [23].…”

Section: Introductionmentioning

confidence: 99%

An analytical study on the synchronization of strange non-chaotic attractors

Sivaganesh¹,

Arulgnanam²

2016

Journal of the Korean Physical Society

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In this paper we present an analytical study on the synchronization dynamics observed in unidirectionally-coupled quasiperiodically-forced systems that exhibit Strange Non-chaotic Attractors (SNA) in their dynamics. The SNA dynamics observed in the uncoupled system is studied analytically through phase portraits and poincare maps. A difference system is obtained by coupling the state equations of similar piecewise linear regions of the drive and response systems.The mechanism of synchronization of the coupled system is realized through the bifurcation of the eigenvalues in one of the piecewise linear regions of the difference system. The analytical solutions obtained for the normalized state equations in each piecewise linear region of the difference system has been used to explain the synchronization dynamics though phase portraits and timeseries analysis. The stability of the synchronized state is confirmed through the Master Stability Function.An explicit analytical solution explaining the synchronization of SNAs is reported in the literature for the first time. PACS numbers: 05.45.Xt, 05.45.-a

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An Analytical Study on the Synchronization of Murali—Lakshmanan—Chua Circuits

Cited by 13 publications

References 21 publications

Generalized analytical solutions for secure transmission of signals using a simple communication scheme with numerical and experimental confirmation

Generalized analytical solutions for secure transmission of signals using a simple communication scheme with numerical and experimental confirmation

Stability enhancement by induced synchronization using transient uncoupling in certain coupled chaotic systems

An analytical study on the synchronization of strange non-chaotic attractors

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