Isochronal synchronization of delay-coupled systems

Schwartz, Ira B.; Shaw, Leah B.

doi:10.1103/physreve.75.046207

Cited by 21 publications

(20 citation statements)

References 37 publications

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“…A feedback delay time that matches the coupling delay between the lasers was proven to stabilize the synchronized solution Schwartz and Shaw, 2007). Under self-feedback, the two lasers play the same role in creating and maintaining synchronization, avoiding, at the same time, the symmetry breaking.…”

Section: Mutually Coupled Lasers Subject To Self-feedbackmentioning

confidence: 97%

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

et al. 2013

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Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

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Section: Mutually Coupled Lasers Subject To Self-feedbackmentioning

confidence: 97%

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

et al. 2013

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“…The question of isochronal synchronization of these nonlinear oscillators (Fischer et al 2006;Klein et al 2006;Rogers-Dakin et al 2006;Schwartz & Shaw 2007;Zhou & Roy 2007;Franz et al 2008) is central to possible applications in sensor networks (Sorrentino & Ott 2008, 2009a. We thus consider coupled oscillators in §4, where the many different configurations, in which even two oscillators may be coupled, are outlined.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

Murphy

Cohen

Ravoori

et al. 2010

Phil. Trans. R. Soc. A.

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We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.

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“…However, if the internal parameters of the coupled systems are adequately tuned, it is possible to obtain anticipated synchronization [5,6], where the receiver system advances in time the dynamics of the transmitter. The intermediate case is known as isochronal synchronization [7] (also called zero-lag synchronization) and corresponds to the situation where both chaotic systems have the same dynamics at exactly the same moment, despite the time lost in the transmission line. Isochronal synchronization has been observed in the dynamics of interconnected cortical areas of the brain [8][9][10] and it has been recently reproduced in small arrays of coupled chaotic lasers [11,12] and electronic circuits [13] where bidirectional coupling was introduced.…”

mentioning

confidence: 99%

Experimental demonstration of bidirectional chaotic communication by means of isochronal synchronization

Wagemakers¹,

Buldú²,

Sanjuán³

2008

Europhys. Lett.

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We give the first experimental demonstration of simultaneous bidirectional communication through chaotic carriers thanks to the phenomenon of isochronal synchronization. Two Mackey-Glass electronic circuits with chaotic behaviour exchange their signals through a coupling line with delay. When the internal feedback of the circuits and the coupling are accurately matched, isochronal synchronization arises. Under this dynamical regime, we introduce a binary message at both outputs and recover it at the opposite circuit. Finally, we discuss the security of this kind of communication system by analyzing the message recovered by a potential eavesdropper.

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Isochronal synchronization of delay-coupled systems

Cited by 21 publications

References 37 publications

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

Experimental demonstration of bidirectional chaotic communication by means of isochronal synchronization

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