Generalized analytical solutions for certain coupled simple chaotic systems

Sivaganesh, G.; Arulgnanam, A.

doi:10.1088/1674-1056/26/5/050502

Cited by 8 publications

(10 citation statements)

References 34 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: 94%

“…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: 94%

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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“…This circuit exhibits a prominent chaotic attractor at the amplitude of the force f 1,2 = 0.695. The chaotic and the synchronization dynamics of the circuit has been studied experimentally, numerically and analytically 18,23 . The chaotic attractors of the drive (blue) and the driven (red) systems with simplified nonlinear elements represented by Eq.…”

Section: B Forced Parallel Lcr Circuit With a Simplified Nonlinear Ementioning

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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“…The stability of complete synchronization observed in coupled chaotic systems is studied using the Master Stability Function (MSF) [15]. The synchronization behavior observed in unidirectionally and mutually coupled MLC circuits have been studied numerically and analytically [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Numerical studies on the synchronization of a network of mutually coupled simple chaotic systems

Sivaganesh,

Arulgnanam,

Seethalakshmi

2019

Preprint

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We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of synchronization behavior. The chaotic attractors of the simple 2 × 2 matrix network exhibiting strange non-chaotic attractors in their synchronization dynamics for smaller values of the coupling strength is reported. Further, the existence of islands of unsynchronized and synchronized states of strange non-chaotic attractors for smaller values of coupling strength is observed. The process of complete synchronization observed in the network with all the systems exhibiting strange non-chaotic behavior is reported. The variation of the slope of the singular continuous spectra as a function of the coupling strength confirming the strange non-chaotic state of each of the system in the network is presented. The stability of complete synchronization observed in the network is studied using the Master Stability Function.

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Generalized analytical solutions for certain coupled simple chaotic systems

Cited by 8 publications

References 34 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

Numerical studies on the synchronization of a network of mutually coupled simple chaotic systems

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