Precision Measurements of Chaotic Electric Circuits

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Precision Measurements of Chaotic Electric
Circuits

• Travis Hoggard
• Katharina Ochterbeck
• Katie M. Reynolds
• Stephen R. Addison
• John E. Gray

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Chua Circuit
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MATLAB Central
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Michael Crosss Chua Circuit
http//www.cmp.caltech.edu/mcc/chaos_new/Chua.htm
l
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Chua Simulations
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Chaotic CircuitsJ.C. Sprott
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J.C. Sprotts Books
Images of a Complex World The Art and Poetry of
Chaos World Scientific Singapore 2005 Chaos
and Time-Series Analysis Oxford University
Press Oxford, 2003 Strange Attractors
Creating Patterns in Chaos MT Books New York,
1993 Out of print, manuscript available at
http//sprott.physics.wisc.edu/fractals/booktext/
Introduction to Modern Electronics John Wiley
Sons New York, 1981 Out of print
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J.C. Sprotts Papers on Chaos
Precision Measurements of a Simple Chaotic
Circuit (with K. Kiers and D. Schmidt), Am. J.
Phys. 72, 503-509 (2004) Chaos in
Fractional-order Autonomous Nonlinear Systems
(with W. M. Ahmad), Chaos, Solitons and Fractals
16, 339-351 (2003) Chaos in a Nonlinear Analog
Computer (with K. Kiers, T. Klein, J. Kolb, and
S. Price), International Journal of Bifurcation
and Chaos 14, 2867-2873 (2004) Simplest Driven
Conservative Chaotic Oscillator (with H. P. W.
Gottlieb), Phys. Lett. A 291, 385-388 (2001) On
the Synchronization of a Class of Electronic
Circuits that Exhibit Chaos (with E. Bai and K.
Lonngren), Chaos, Solitons and Fractals 13,
1515-1521 (2002) Algebraically Simple Chaotic
Flows (with S. J. Linz), Int. J. Chaos Theory and
Appl. 5, 3-22 (2000) Simple Chaotic Systems and
Circuits, Am. J. Phys. 68, 758-763 (2000) A New
Class of Chaotic Circuit, Phys. Lett. A 266,
19-23 (2000) Elementary Chaotic Flow (with S. J.
Linz), Phys. Lett. A 259, 240-245
(1999) Controlling Chaos in a High Dimensional
System with Periodic Parametric Perturbations
(with K. A. Mirus), Phys. Lett. A 254, 275-278
(1999) Controlling Chaos in Low- and
High-dimensional Systems with Periodic Parametric
Perturbations (with K. A. Mirus), Phys. Rev. E
59, 5313-5324 (1999) Artificial Neural Net
Attractors, Comput. Graphics 22, 143-149
(1998) Some Simple Chaotic Jerk Functions, Am.
J. Phys. 65, 537-543 (1997) Simplest Dissipative
Chaotic Flow, Phys. Lett. A 228, 271-274
(1997) Some Simple Chaotic Flows, Phys. Rev. E
50, R647-R650 (1994) Predicting the Dimension of
Strange Attractors, Phys. Lett. A 192, 355-360
(1994) How Common is Chaos?, Phys. Lett. A 173,
21-24 (1993) Extraction of Dynamical Equations
from Chaotic Data (with G. Rowlands), Physica D
58, 251-259 (1992)
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Sprott Circuits
Sprott circuits are described by the nonlinear
jerk equation
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Kiers, Schmidt, Sprott Circuit
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Kiers, Schmidt, Sprott Circuit
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Kiers, Schmidt, Sprott Circuit
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Kiers, Schmidt, Sprott Circuit
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Circuit and Differential Equation
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Circuit and Differential Equation
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Circuit and Differential Equation
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Different circuits for the nonlinear element D(x)
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Kiers, Schmidt, Sprott D(x)
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Kiers, Schmidt, Sprott D(x)
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D(x)
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Power Supplies
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Power Supplies
On power supplies used for laboratory
demonstration of chaotic electronic
circuits Prodyot Kumar Roy Arijit
Basuray Emanuel Gluskin American Journal of
Physics 73, 1082-1085 (2005)
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Conclusions

• We can build chaotic circuits that work reliably

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Conclusions

• We can build chaotic circuits that work reliably
• We can make these circuit operate in both chaotic
  and periodic regimes

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Conclusions

• We can build chaotic circuits that work reliably
• We can make these circuit operate in both chaotic
  and periodic regimes
• The Sprott circuits are useful for investigating
  synchronization

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Conclusions

• We can build chaotic circuits that work reliably
• We can make these circuit operate in both chaotic
  and periodic regimes
• The Sprott circuits are useful for investigating
  synchronization
• The Sprott circuits are useful for experimental
  investigations of chaos

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Future Work
So what does come next?