Experimental Demonstration of Anticipating Synchronization in Chaotic Semiconductor Lasers with Optical Feedback

Sivaprakasam, S.; Em, Shahverdiev; Ps, Spencer; Ka, Shore

doi:10.1103/physrevlett.87.154101

Cited by 201 publications

(92 citation statements)

References 17 publications

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“…That is, synchronization is exhibited between drive and time delayed response system, so that in this manner the slave dynamics act as a predictor of the master dynamics. Following Voss, 5 these anticipating synchronization phenomena have been observed experimentally in an electronic circuit 6 and in chaotic semiconductor diode lasers 7 and numerically in chaotic external cavity semiconductor lasers. 8 Further, recently several other papers on synchronization of systems containing delays have appeared.…”

Section: Introductionmentioning

confidence: 85%

“…All examples of anticipating synchronization mentioned above [5][6][7][8] essentially dealt with one-dimensional systems with delay in the state and an asymptotically stable linear part. Oguchi and Nijmeijer 17 recently generalized this by considering anticipating master-slave synchronization where the master is a higher-dimensional chaotic time-delay system with time-delayed states entering linearly and a linear part that is not necessarily asymptotically stable.…”

Section: Introductionmentioning

confidence: 99%

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Anticipating synchronization of chaotic Lur’e systems

Huijberts

Nijmeijer

Oguchi

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper we consider the anticipating synchronization of chaotic time-delayed Lur'e-type systems in a master-slave setting. We introduce three scenarios for anticipating synchronization, and give sufficient conditions for the existence of anticipating synchronizing slave systems in terms of linear matrix inequalities. The results obtained are illustrated on a time-delayed Rössler system and a time-delayed Chua oscillator. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2710964͔In their ground breaking 1990 paper, Pecora and Carroll 1 showed that, in spite of sensitive dependence on initial conditions, coupled chaotic systems can synchronize. Following this work, in the last decades considerable interest in the notion of synchronization of complex or chaotic systems has arisen. Among others, perhaps the main motivation so far seems to lie in potential applications regarding secure or private communications, though the number of reported applications is still limited to date. On the other hand synchronization appears in numerous different ways, most notably in biological applications (heart beat, brain activity, neural activity, walking, etc.), nature (planetary motion), physics (organ pipes, etc.) and engineering (coordinated robot motion, etc.). 2-4 More recently, it was observed by Voss 5 that coupled chaotic Ikeda time-delay systems can exhibit what is called anticipating synchronization in that the state of one of the systems synchronizes with the future state of the other system, which allows one to predict the state of the latter system in spite of the inherent unpredictability of chaotic systems. In many applications where synchronization seems to be essential, the coupling between systems naturally contains a small amount of delay that nevertheless does not prevent synchronization from occurring. In this regard one may think about transport delay (e.g., chemical transport between cells in a living organism) or other forms of delay like optical delay in the synchronized movement of swarms of birds. Another example occurs when multiple agents, like, e.g., robots, share a communication network, which in principle will lead to a natural delay in the execution of (shared) tasks. It is therefore of interest to investigate how anticipating synchronization can be achieved for general classes of complex or chaotic systems. In this paper we will consider a wide class of chaotic time-delay systems, so-called Lur'e systems, and discuss when and how one can design anticipating synchronization schemes for these systems.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Anticipating synchronization of chaotic Lur’e systems

Huijberts

Nijmeijer

Oguchi

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Cross-correlation statistics between the two intensities showed clear maxima at delay times consisting of the difference between the feedback and the coupling delay. Anticipatory responses in the presence of stochastic effects have been observed in models of excitable media [11], as well as in experiments of coupled semi-conductor lasers in a transmitter-receiver configuration [29]. When the zero lag state is unstable and achronal synchronization occurs, the situation may be further complicated by switching between leader and follower.…”

Section: Introductionmentioning

confidence: 97%

Isochronal synchronization of delay-coupled systems

Schwartz

Shaw

2007

Phys. Rev. E

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We consider small network models for mutually delay-coupled systems which typically do not exhibit stable isochronally synchronized solutions. We show analytically and numerically that for certain coupling architectures which involve delayed self feedback to the nodes, the oscillators become isochronally synchronized. Applications are shown for both incoherent pump coupled lasers and spatio-temporal coupled fiber ring lasers.

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“…In this regime, two dynamical systems synchronize in such a way that the slave system anticipates the trajectory of the master. Anticipating synchronization has been studied theoretically and experimentally in many systems, e. g., in chaotic semiconductor lasers [12][13][14], in electronic circuits [15], in excitable systems [16], in coupled inertial ratchets [17], and in neural networks [18,19]. It is remarkable that neither nonlinearity nor chaotic dynamics of the master and drive systems are the necessary condition for the anticipating synchronization [20].…”

Section: Introductionmentioning

confidence: 99%

Anticipating of chaotic states via anti-phase diagonal coupling

Pyragienė¹,

Pyragas²

2010

Lithuanian J. Phys.

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Anticipating synchronization is considered as a tool for a real-time forecasting of chaotic dynamics. An anti-phase diagonal coupling scheme is introduced in order to supply the long-term prediction of behaviour of a drive system. The efficiency of such a scheme is studied analytically using a simple model of unstable spiral and justified numerically for two unidirectionally coupled chaotic Rössler systems. The maximum prediction time attained with our algorithm equals to the half of characteristic period of chaotic oscillations.

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Experimental Demonstration of Anticipating Synchronization in Chaotic Semiconductor Lasers with Optical Feedback

Cited by 201 publications

References 17 publications

Anticipating synchronization of chaotic Lur’e systems

Anticipating synchronization of chaotic Lur’e systems

Isochronal synchronization of delay-coupled systems

Anticipating of chaotic states via anti-phase diagonal coupling

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