Synchronizing Hyperchaos with a Scalar Transmitted Signal

Peng, Jianhua; Ding, E. J.; Ding, Mingzhou; Yang, Weiming

doi:10.1103/physrevlett.76.904

Cited by 342 publications

(140 citation statements)

References 21 publications

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“…21 There was speculation that one would need as many drive signals as there were positive Lyapunov exponents in the original system. The paper by Peng et al cleared that controversy up.…”

Section: B a Conjecture Disproven And Imposed Bifurcationsmentioning

confidence: 99%

Synchronization of chaotic systems

Pecora

Carroll

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

439

326

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We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.

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“…21 There was speculation that one would need as many drive signals as there were positive Lyapunov exponents in the original system. The paper by Peng et al cleared that controversy up.…”

Section: B a Conjecture Disproven And Imposed Bifurcationsmentioning

confidence: 99%

Synchronization of chaotic systems

Pecora

Carroll

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

439

326

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show abstract

“…Later, Perez and Cerdeira [107] have shown that messages masked by low-dimensional chaotic processes can be intercepted and extracted. Therefore, the attention was directed to the implementation of the Pecora and Carrols (PC) idea to higher dimensional systems [141] with the hope that increased unpredictability could improve security in the communication.…”

Section: The Adaptive Synchronization Of Chaos For Secure Communicationmentioning

confidence: 99%

The control of chaos: theory and applications

et al. 2000

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“…Chaotic Colpitts oscillator has only one positive LE. Meanwhile for chaos based communications more complicated oscillators, characterized by multiple positive LE are needed [3,4]. Dynamical systems having more than one positive LE are called hyperchaotic ones.…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos in coupled Colpitts oscillators

Čenys¹,

Tamaševičius²,

Baziliauskas

et al. 2003

Chaos, Solitons & Fractals

114

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The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R k . The hyperchaotic output signal vðtÞ is a linear combination, specifically the mean of the individual chaotic signals, vðtÞ ¼ ðv 1 þ v 2 Þ=2. The corresponding differential equations have been derived. The results of both, numerical simulations and hardware experiments are presented. The coupling coefficient k / 1=R k should be small to avoid mutual synchronisation of the individual oscillators. The spectrum of the Lyapunov exponents (LE) have been calculated versus the coefficient k. For weakly coupled oscillators there are two positive LE indicating hyperchaotic behaviour of the overall system.

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Synchronizing Hyperchaos with a Scalar Transmitted Signal

Cited by 342 publications

References 21 publications

Synchronization of chaotic systems

Synchronization of chaotic systems

The control of chaos: theory and applications

Hyperchaos in coupled Colpitts oscillators

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