The Anatomy of the Chua circuit
(2014) FYSK01 20141Department 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:
http://lup.lub.lu.se/studentpapers/record/4499949
 author
 Lavröd, Jakob ^{LU}
 supervisor

 Sven Åberg ^{LU}
 organization
 course
 FYSK01 20141
 year
 2014
 type
 M2  Bachelor Degree
 subject
 keywords
 Chaos, Chua circuit, Lyapunov exponent, Validation
 language
 English
 id
 4499949
 date added to LUP
 20140625 11:15:45
 date last changed
 20141113 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}, }