Evidence of homoclinic chaos in the plasma of a glow discharge

Bräun, Thomas; Lisboa, Jorge Amoretti; Gallas, Jason A. C.

doi:10.1103/physrevlett.68.2770

Cited by 76 publications

(37 citation statements)

References 18 publications

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“…As indicated schematically by the numbers in Fig. 2a, when moving along the dark central bodies of the islands one observes series of period-adding cascades of bifurcations, a characteristic signature of the experimentally elusive and rather challenging homoclinic route to chaos [23,24,25,26,27,28,29,30]. Note that the periodicity in these cascades increases by 4, the same periodicity characterizing the region of periodicity that exists to the left of the accumulation boundary.…”

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confidence: 97%

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Accumulation horizons and period adding in optically injected semiconductor lasers

Bonatto

Gallas

2007

Phys. Rev. E

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We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable accumulation horizons: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as e.g. secure communications. [12] reported diagrams obtained by numerical integration of the rate equations for an optically injected semiconductor laser showing some islands of periodic laser signals embedded in a sea of chaos. These important findings raise an interesting question concerning the precise structuring of laser chaotic phases. In fact, this question is the tip of a much wider problem that we consider here.Phase diagrams for discrete-time models described by mappings are common nowadays [13,14]. But the much more difficult problem of building detailed phase diagrams for models ruled by sets of nonlinear differential equations has been much less investigated. Of course, diagrams recording complex bifurcations and providing valuable insight for a few of the lowest periods have been obtained in a number of in-depth bifurcation studies using powerful continuation methods [7,15,16,17]. However, complete diagrams, discriminating simultaneously regions of arbitrarily high periods and regions with chaotic phases, remain essentially unexplored for continuous-time autonomous models. This is the problem we attack here.Our numerical simulations revealed surprising regularities existing inside the chaotic phases of the laser. As illustrated in Figs. 1 and 2, the parameter space has wide regions characterized by chaotic solutions. These chaotic phases contain both single accumulations as well as accumulations of accumulations. More specifically, chaotic laser phases are riddled with infinite sequences of periodadding cascades, each one converging toward curves that look simple (structureless), denoted "accumulation horizons", for simplicity. One example is indicated by the arrow marked A in Fig. 2a. From a theoretical point of view, a key novelty here is that the differential equations ruling the laser are autonomous equations, i.e., they do not involve time explicitly. Thus, the remarkable organization of the parameter space reported here must originate from an intrinsic interplay between variables and parameters of the laser. We found accumulation horizons to exist abundantly also in electronic circuits, atmospheric and chemical oscillators, and several other systems [18]. To fix ideas, here we focus just on the laser case. Incidentally, we mention that accumulation cascades in semiconductor lasers have been investigated by Krauskopf and Wieczorek [17] quite recently. However, their accumulations are of a very different nature than ours [19].The laser w...

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confidence: 97%

“…3, obtained when moving along the upper dotted path in Fig. 2a, show period-adding cascades with the characteristic alternation of chaos and periodicity [23,24,25,26,27,28,29,30]. Numbers labeling periodic windows refer to the number of peaks present in one period of the respective variable.…”

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confidence: 99%

Accumulation horizons and period adding in optically injected semiconductor lasers

Bonatto

Gallas

2007

Phys. Rev. E

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“…Chaos in gas discharges systems, other than low-temperature atmospheric plasmas, is known with its nonlinear characteristics comprehensively studied in various laboratory plasmas including low-pressure processing plasmas [16][17][18] and high-pressure arcs [19,20]. However, in most cases, the plasmas studied are often undriven, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…However, in most cases, the plasmas studied are often undriven, i.e. the chaotic behavior arises from self-oscillation within steady-state (dc) plasma [16][17][18][19][20][21] although chaos in driven plasmas has also been reported [22]. In the case of atmospheric-pressure DBD jets, the discharge is generated using a fixed frequency; consequently the system can be considered to be driven.…”

Section: Introductionmentioning

confidence: 99%

Chaos in atmospheric-pressure plasma jets

Walsh¹,

Iza²,

Janson³

et al. 2012

Plasma Sources Sci. Technol.

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Abstract:We report detailed characterization of a low-temperature atmosphericpressure plasma jet that exhibits regimes of periodic, quasi-periodic and chaotic behaviors. Power spectra, phase portraits, stroboscopic section and bifurcation diagram of the discharge current combine to comprehensively demonstrate the existence of chaos, and this evidence is strengthened with a nonlinear dynamics analysis using two control parameters that maps out periodic, period-multiplication, and chaotic regimes over a wide range of the input voltage and gas flow rate. In addition, optical emission signatures of excited plasma species are used as the second and independent observable to demonstrate the presence of chaos and period-doubling in both the concentrations and composition of plasma species, suggesting a similar array of periodic, quasi-periodic and chaotic regimes in plasma chemistry. The presence of quasi-periodic and chaotic regimes in structurally unbounded low-temperature atmospheric plasmas not only is important as a fundamental scientific topic but also has interesting implications for their numerous applications. Chaos may be undesirable for industrial applications where cycle-tocycle reproducibility is important, yet for treatment of cell-containing materials including living tissues it may offer a novel route to combat some of the major challenges in medicine such as drug resistance. Chaos in low-temperature atmospheric plasmas and its effective control are likely to open up new vistas for medical technologies.2

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“…In many cases [4][5][6][7] these phenomena can be understood in terms of a paradigmatic model known as the Shilnikov homoclinic chaos (HC) [8]. HC may arise in three-dimensional phase space when a growing periodic orbit approaches a saddle-focus becoming homoclinic to it, i.e.…”

Section: Introductionmentioning

confidence: 99%

Chaotic and Mixed Mode Oscillation Scenarios in Semiconductor Devices: Generation and Synchronization

et al. 2012

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We demonstrate the existence of chaotic spiking and mixed mode oscillations sequences in the dynamics of semiconductor devices (laser diode and light emitting diode) with ac-coupled optoelectronic feedback. We eventually show that this regime is the result of an incomplete homoclinic scenario to a saddle-focus, where an exact homoclinic connection does not occur. The synchronization scenarios have been shown.

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Evidence of homoclinic chaos in the plasma of a glow discharge

Abstract: Homoclinic chaos is sho~n to occur in the electric current measured on an electrical discharge in argon. We report a clear sequence of four hesitations followed by a reverse period doubling. The experimental signals are used io construct return time-and time of fl-igh-t

Cited by 76 publications

References 18 publications

Accumulation horizons and period adding in optically injected semiconductor lasers

Accumulation horizons and period adding in optically injected semiconductor lasers

Chaos in atmospheric-pressure plasma jets

Chaotic and Mixed Mode Oscillation Scenarios in Semiconductor Devices: Generation and Synchronization

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