Chua's oscillator: A compendium of chaotic phenomena

Pivka, Ladislav; Wu, Chai Wah; Huang, Anshan

doi:10.1016/0016-0032(94)90087-6

Cited by 46 publications

(18 citation statements)

References 35 publications

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“…For example, in the case of Chua circuit, for most cases shown in Tables 1 and 2 in [20] we obtain the Kaplan-Yorke fractal dimensions, D KY , in the interval 2.00-2.25, but there are also cases with D KY equal 2.32, 2.40 or even 2.94. Other oscillators described by systems of three ODEs with only quadratic nonlinearities yield chaotic strange attractors with fractal dimensions D KY that span practically the whole interval from 2 to 3.…”

Section: Comparison Of Fractal Dimensionsmentioning

confidence: 99%

Circuits with Oscillatory Hierarchical Farey Sequences and Fractal Properties

Marszałek

2012

Circuits Syst Signal Process

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We present two dual oscillating circuits having a wide spectrum of dynamical properties but relatively simple topologies. Each circuit has five bifurcating parameters, one nonlinear element of cubic current-voltage characteristics, one controlled element, LCR components and a constant biasing source. The circuits can be considered as two coupled oscillators (linear and nonlinear) that form dual jerk circuits. Bifurcation diagrams of the circuits show a rather surprising result that the bifurcation patterns are of the Farey sequence structure and the circuits' dynamics is of a fractal type. The circuits' fractal dimensions of the box counting (capacity) algorithm, Kaplan-Yorke (Lyapunov) type and its modified (improved) version are all estimated to be between 2.26 and 2.52. Our analysis is based on numerical calculations which confirm a close relationship of the circuits' bifurcation patterns with those of the Ford circles and Stern-Brocot trees.

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Section: Comparison Of Fractal Dimensionsmentioning

confidence: 99%

Circuits with Oscillatory Hierarchical Farey Sequences and Fractal Properties

Marszałek

2012

Circuits Syst Signal Process

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“…(4.12)-(4.14). Scale the circuit equations into a dimensionless form suitable for implementation on an FPGA [6]. 1 Incommensurate frequencies ω 1 and ω 2 imply that the ratio ω1 ω2 ∈ R\Q.…”

Section: Example 41mentioning

confidence: 99%

Bifurcations

Muthuswamy¹,

Banerjee²

2015

A Route to Chaos Using FPGAs

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“…Obviously, from an implementation point of view, chaotic systems with simpler structures deserve more attention, for which 3D autonomous systems are of the lowest possible dimensions. Therefore, many 3D chaotic systems have been established, such as Chua's circuit [7,8], Chen system [9], etc. To stabilize the oscillations or to utilize chaos, how to control these systems to meet the need is an important task in nonlinear dynamics.…”

Section: Introductionmentioning

confidence: 99%