Experimental evidence for a torus breakdown in a glow discharge plasma

Letellier, Christophe; Dinklage, A.; El-Naggar, Hala I.; Wilke, Charles R.; Bonhomme, G.

doi:10.1103/physreve.63.042702

Cited by 21 publications

(13 citation statements)

References 8 publications

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“…The experimental work [4] is performed in a cylindrical dc glow discharge tube with r =1 cm, discharge length L = 60 cm, and I < 60 A. The striations can be observed by the light emission of excited atoms in the positive column by means of a charge-coupled device (CCD), see Fig.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis and Simulation Analysis for Space‐Time Data

Hassouba¹,

Al-Naggar

et al. 2006

Contrib. Plasma Phys.

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Spatio temporal dynamics of the positive column of a dc neon glow discharge is studied and investigated experimentally and theoretically. Spatio temporal analysis by means of biorthogonal decomposition method (BOD) gives insights into the mechanism of irregularity and can be employed for characterization of spatio-temporal complexity. In the weak nonlinear region, the wave dynamics is approximated by an amplitude equation of the Ginzburg-Landau equation (CGLE) with complex coefficients and an additional integral term based on a fluid model. In the present work we deal with irregular spatio-temporal data. A comparison between the numerical analysis of the experimental data and simulation results are studied. A good agreement between the dynamical behaviour for experimental space-time data and theoretical simulation space-time results was obtained.

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Section: Introductionmentioning

confidence: 99%

Numerical Analysis and Simulation Analysis for Space‐Time Data

Hassouba¹,

Al-Naggar

et al. 2006

Contrib. Plasma Phys.

Self Cite

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“…In the present work we extend these results to threedimensional attractors of higher genus (g > 1). These include many attractors generated by autonomous dynamical systems with two-fold or higher-fold symmetry [4,16,17,18]. We find the analogs of parity and global torsion, but do not discuss knot type, but all embeddings reveal the same stretching and folding mechanism.…”

Section: Introductionmentioning

confidence: 93%

Global topology from an embedding

Gilmore

Letellier

Romanazzi

2007

J. Phys. A: Math. Theor.

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An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically equivalent. In a previous work we showed how the original and reconstructed attractors can differ when the original is three-dimensional and of genus-one type.In the present work we extend this result to three-dimensional attractors of arbitrary genus. This result describes symmetries exhibited by the Lorenz attractor and its reconstructions.

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“…6 appear to converge on the z axis in this region (100 < z < 200). In fact, the trajectory never reaches the z axis, since it is an invariant set [10]. If it did intersect the z axis, it would extend to z → ∞ and the attractor would be unstable.…”

Section: Poincaré Sectionmentioning

confidence: 99%

Poincaré sections for a new three-dimensional toroidal attractor

Letellier¹,

Gilmore²

2008

J. Phys. A: Math. Theor.

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A new 3D autonomous dynamical system proposed by Dequan Li [Physics Letters A, 372, 387, 2008.] produces a chaotic attractor whose global topological properties are unusual. The attractor has a rotation symmetry and only a single real fixed point for the parameters used in his study. The symmetric, complex pair of fixed points cannot be ignored: they play a major role in organizing the motion on a surface of peculiar toroidal type. We describe this attractor, propose a simple, intuitive model to understand it, show that it is of toroidal type and of genus three, construct a global Poincaré surface of section with two disjoint components and use this section to locate unstable periodic orbits and determine their topological period. We also show that its image attractor is of genus one and supports flow on a simple wrinkled torus. Finally, we use the interplay between the original covering attractor and its image as an aid to understand why the Li attractor is of genus-three type.

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Experimental evidence for a torus breakdown in a glow discharge plasma

Cited by 21 publications

References 8 publications

Numerical Analysis and Simulation Analysis for Space‐Time Data

Numerical Analysis and Simulation Analysis for Space‐Time Data

Global topology from an embedding

Poincaré sections for a new three-dimensional toroidal attractor

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