Detecting orbits of high periods from numerical solutions of the Rossler system

Kukharenko, B. G.

doi:10.1109/phycon.2005.1514111

Cited by 2 publications

(7 citation statements)

References 12 publications

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“…Note, (see in the following) that in the framework of this analysis H k-s coincides with the Kolmogorov deferential entropy of the PDF ( [17], pages 542-543, 839).…”

Section: Approximate Approach For Variance Calculationmentioning

confidence: 75%

“…Let us consider the results of simulations of the Rössler attractor with the following parameters: a= 0.2, b=0.2, c = 5.7 [14,17].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The non-hyperbolic attractors are rather sensitive to variations of their parameters: the character of chaos can change drastically (from spiral to punnel [7,17]), for example, for Rössler attractor when the "c" parameter (see below) changes from 5.7 to 10. Nevertheless the existence of the stationary measure for the Rössler attractor was confirmed in [7].…”

Section: Basics Of the Chaotic Attractors Theory Degene-rated Cumentioning

confidence: 99%

“…For a linear matrix A the Lyapunov exponents are defined by its eigen-values ( [17], pages 542-543).…”

Section: Approximate Approach For Variance Calculationmentioning

confidence: 99%

“…The non-linear system describing the chaotic behavior of the Rössler attractor has to be statistically linearized ( [17], page 760).…”

mentioning

confidence: 99%

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Cumulant Analysis of Rössler Attractor and its Applications

Kontorovich¹,

Beltrán²,

Aguilar³

et al. 2009

TOCSJ

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This paper is dedicated to the statistical analysis of the chaos, generated by Rössler attractor, based on the socalled "Degenerated Cumulant Equations" method. The approach is illustrated by the calculus of the first cumulants, which are necessary to create an approximation of the Probability Density Function (PDF), applying the Gramm-Charlier series, the model distribution method, etc. An approximate method for the variance calculation at the output of the Rössler strange attractor is presented as well. The latter is based on the Kolmogorov-Sinai entropy estimated by the Lyapunov exponents for a statistically linearized chaotic system. Finally, an application using Rössler attractor output signals to model Radio Frequency Interferences (RFI) provided by Peripherical Component Interface express (PCIe) serial bus of high speed interconnects of Laptops and Desktops is presented.

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“…Note, (see in the following) that in the framework of this analysis H k-s coincides with the Kolmogorov deferential entropy of the PDF ( [17], pages 542-543, 839).…”

Section: Approximate Approach For Variance Calculationmentioning

confidence: 75%

“…Let us consider the results of simulations of the Rössler attractor with the following parameters: a= 0.2, b=0.2, c = 5.7 [14,17].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%