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The Anatomy of the Chua circuit

Lavröd, Jakob LU (2014) FYSK01 20141
Department of Physics
Abstract (Swedish)
The Chua circuit, known to exhibit chaotic behaviour, has been constructed and studied. The goal was to investigate
the experimental underpinning of the theory. The component relationship of the resistors, capacitors, inductors and
operational amplifiers have been measured and established within their domain of validity.
The system equations themselves cannot be directly validated through a traditional simulation vs. experimental
study due to the chaotic property. Instead, a novel procedure is proposed where the system variables are split into
groups, with each group being validated by obtaining the variables outside the group directly from experimental data.
The method decisively confirms the equations and parameters values to be... (More)
The Chua circuit, known to exhibit chaotic behaviour, has been constructed and studied. The goal was to investigate
the experimental underpinning of the theory. The component relationship of the resistors, capacitors, inductors and
operational amplifiers have been measured and established within their domain of validity.
The system equations themselves cannot be directly validated through a traditional simulation vs. experimental
study due to the chaotic property. Instead, a novel procedure is proposed where the system variables are split into
groups, with each group being validated by obtaining the variables outside the group directly from experimental data.
The method decisively confirms the equations and parameters values to be correct.
To streamline the theoretical computations, the special piecewise linear structure of the system equations is used
to obtain local analytical solutions, which are then pieced together by equation solving. Using the resistance as the
control parameter, the different solutions to the equations are classified and qualitatively explained. A number of
experimental tests are performed to investigate the correspondence between theory and experiments; the invariance
under parity inversion, the position of the Hopf bifurcation and the equilibrium voltage as a function of resistance.
Finally, chaos is quantified using the Lyapunov exponent. As its definition requires a metric, such is proposed
based on energy consideration. The piecewise linear structure of the equation provides a very simple formula for the
Lyaupnov exponent in terms of averaging over the Generalized Rayleigh quotient along a trajectory. The Lyaupnov
exponent is evaluated as a function of resistance and compared with the qualitative conclusions about the circuit. (Less)
Please use this url to cite or link to this publication:
author
Lavröd, Jakob LU
supervisor
organization
course
FYSK01 20141
year
type
M2 - Bachelor Degree
subject
keywords
Chaos, Chua circuit, Lyapunov exponent, Validation
language
English
id
4499949
date added to LUP
2014-06-25 11:15:45
date last changed
2014-11-13 09:52:04
@misc{4499949,
  abstract     = {The Chua circuit, known to exhibit chaotic behaviour, has been constructed and studied. The goal was to investigate
the experimental underpinning of the theory. The component relationship of the resistors, capacitors, inductors and
operational amplifiers have been measured and established within their domain of validity.
The system equations themselves cannot be directly validated through a traditional simulation vs. experimental
study due to the chaotic property. Instead, a novel procedure is proposed where the system variables are split into
groups, with each group being validated by obtaining the variables outside the group directly from experimental data.
The method decisively confirms the equations and parameters values to be correct.
To streamline the theoretical computations, the special piecewise linear structure of the system equations is used
to obtain local analytical solutions, which are then pieced together by equation solving. Using the resistance as the
control parameter, the different solutions to the equations are classified and qualitatively explained. A number of
experimental tests are performed to investigate the correspondence between theory and experiments; the invariance
under parity inversion, the position of the Hopf bifurcation and the equilibrium voltage as a function of resistance.
Finally, chaos is quantified using the Lyapunov exponent. As its definition requires a metric, such is proposed
based on energy consideration. The piecewise linear structure of the equation provides a very simple formula for the
Lyaupnov exponent in terms of averaging over the Generalized Rayleigh quotient along a trajectory. The Lyaupnov
exponent is evaluated as a function of resistance and compared with the qualitative conclusions about the circuit.},
  author       = {Lavröd, Jakob},
  keyword      = {Chaos,Chua circuit,Lyapunov exponent,Validation},
  language     = {eng},
  note         = {Student Paper},
  title        = {The Anatomy of the Chua circuit},
  year         = {2014},
}