Phase synchronization and polarization ordering of globally coupled oscillators

Scire, A.; Colet, Pere; Miguel, M. San

doi:10.1103/physreve.70.035201

Cited by 5 publications

(1 citation statement)

References 27 publications

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“…Integration of polarization encoding/decoding is therefore relevant. Polarization chaos also shows many advantageous properties for chaos multiplexing 32 , chaos synchronization and security 31 and ordering in globally coupled oscillators 50 which now can be explored and practically tackled.…”

Section: Discussionmentioning

confidence: 99%

Deterministic polarization chaos from a laser diode

et al. 2012

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Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect -i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single-and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.The discovery of deterministic chaos -i.e. the aperiodic deterministic dynamics of a nonlinear system showing sensitivity to initial conditions -has been a major paradigm shift overthrowing two centuries of Laplacian viewpoint of dynamical systems [1][2][3][4][5] . Looking into a system behavior with the use of chaos theory has helped to interpret and control many of such ordered or disordered behaviors in our present day life, such as the bifurcations leading to epilepsy and cancer 6 , the stabilization of cardiac arrhythmias 7 , and the improvement of complex behavioral patterns in robotics 8 .Soon after the invention of the laser, the possibility to observe light chaos raised attention. In 1975, Haken discovered an analogy between the Maxwell-Bloch equations for lasers and the Lorenz equations showing chaos 9 . The Maxwell-Bloch equations are three equations for the field E, the polarization P and the carrier inversion N, each with its own relaxation time. However, while in Lorenz equations the relaxation times of the dynamical variables are of similar order of magnitude, they may take very different values in lasers. If one variable relaxes much faster than the others, this variable is adiabatically eliminated, hence resulting in a reduced number of dynamical equations. Therefore, so-called class A (ex: He-Ne, Ar and Dye), class B (ex: Nd:YAG, CO2 and semiconductor) or class C (ex: NH3) lasers have dynamics governed either by a single equation for the field, two equations for the field and population inversion or the full set of equations, respectively. In class A or class B laser systems chaos cannot be observed unless one adds one or several independent control parameters 10 . Chaos has then been reported in, for example, free-running NH3 lasers 11 , He-Ne lasers with modulation of the external field 12 , CO2

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Section: Discussionmentioning

confidence: 99%

Deterministic polarization chaos from a laser diode

et al. 2012

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Consensus control for a class of networks of dynamic agents

Xie

Wang

2006

Intl J Robust & Nonlinear

487

263

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SUMMARYIn this paper, the consensus problems for networks of dynamic agents are investigated. The agent dynamics is adopted as a typical point mass model based on the Newton's law. The average-consensus problem is proposed for such class of networks, which includes two aspects, the agreement of the states of the agents and the convergence to zero of the speeds of the agents. A linear consensus protocol for such networks is established for solving such a consensus problem that includes two parts, a local speed feedback controller and the interactions from the finite neighbours. Two kinds of topology are discussed: one is fixed topology, the other is switching one. The convergence analysis is proved and the protocol performance is discussed as well. The simulation results are presented that are consistent with our theoretical results.

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Consensus Control for Networks of Dynamic Agents via Active Switching Topology

Xie

Wang

2005

Lecture Notes in Computer Science

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Abstract. This paper investigates the average-consensus problem for networks of dynamic agents. A consensus protocol based on active switching topology for solving the average-consensus problem of the network is proposed. Within such a topology, a finite set of candidate unconnected graphs is used and we change the topology actively according to the state of the network. The advantage of such mechanism is that it decreases the communication complexity/cost dramatically. The simulation results are presented that are consistent with our theoretical results.

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Phase synchronization and polarization ordering of globally coupled oscillators

Cited by 5 publications

References 27 publications

Deterministic polarization chaos from a laser diode

Deterministic polarization chaos from a laser diode

Consensus control for a class of networks of dynamic agents

Consensus Control for Networks of Dynamic Agents via Active Switching Topology

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