Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A.N.; Selvaraj, S.

doi:10.3938/jkps.72.1121

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…The chaotic signal v(t) has been used as the carrier wave of this unidirectional scheme. In the absence of the signal s(t), a synchronized chaotic behavior is observed in the coupled system between v(t) and v (t) [27], for = 1105.5, C = 10.31 nF, L = 51.3 mH, R = 2211 Ω, F 1,2 = 1.7 V, ν 1,2 = 5500 Hz, G a = −0.56 mS, G b = 2.5 mS and B p = ±3.8 V.…”

Section: Resultsmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

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: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Explicit Analytical Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

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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“…When compared with unidirectional coupling synchronization, bidirectional (or mutual) coupling synchronization is more attractive due to the fact that it is ready to implement in practice. Recently, Sivaganesh et al proposed the synchronization of a network of mutually coupled chaotic systems, in which the synchronization behaviour changes as the coupling parameters change [21].…”

Section: Introductionmentioning

confidence: 99%

The Synchronization of N Cascade‐Coupled Chaotic Systems

et al. 2019

Complexity

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In this paper, we investigate a novel synchronization method, which consists of n (n ≥ 2) cascade-coupled chaotic systems. Furthermore, as the number of chaotic systems decreases from n to 2, the proposed synchronization will transform into bidirectional coupling synchronization. Based on Lyapunov stability theory, a general criterion is proposed for choosing the appropriate coupling parameters to ensure cascading synchronization. Moreover, 4 Lü systems are taken as an example and the corresponding numerical simulations demonstrate the e ectiveness of our idea.

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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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Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

Cited by 6 publications

References 22 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

The Synchronization of N Cascade‐Coupled Chaotic Systems

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

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