Sinusoidal excitation on the Chua's circuit simulation of limit cycles and chaos

Erik Lindberg

doi:10.1109/ISCAS.1994.409513

Sinusoidal excitation on the Chua's circuit simulation of limit cycles and chaos

Erik Lindberg

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Abstract

Experiments with modelling and simulation of sinusoidal excitation on Chua's circuit are presented. It is demonstrated that the behaviour of the circuit is based on the interaction of two different kinds of energy balance: chaotic behaviour based on a balance between two unstable “states of charging”, and stable limit cycle behaviour based on the balance between the energy lost in the regions with mainly positive losses and the energy gained in the regions with mainly negative losses. Convergence problems observed in connection with simulation of the ideal piecewise-linear model are solved by means of a smooth continuous model of the nonlinear element based on the ideal operational amplifier model instead of a polynomial approximation. The movements of the eigenvalues as functions of the nonlinear resistance are found. Stable limit cycles of periods 1, 2, 3 and 5 are found by introducing losses

Original language	English
Title of host publication	Proceedings of the IEEE International Symposium on Circuits and Systems
Volume	Volume 6
Publisher	IEEE
Publication date	1994
Pages	5-8
ISBN (Print)	07-80-31915-X
DOIs	https://doi.org/10.1109/ISCAS.1994.409513
Publication status	Published - 1994
Event	1994 IEEE International Symposium on Circuits and Systems - London, United Kingdom Duration: 30 May 1994 → 2 Jun 1994 http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=3224

Conference

Conference	1994 IEEE International Symposium on Circuits and Systems
Country/Territory	United Kingdom
City	London
Period	30/05/1994 → 02/06/1994
Internet address	http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=3224

Bibliographical note

Copyright: 1994 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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title = "Sinusoidal excitation on the Chua's circuit simulation of limit cycles and chaos",

abstract = "Experiments with modelling and simulation of sinusoidal excitation on Chua's circuit are presented. It is demonstrated that the behaviour of the circuit is based on the interaction of two different kinds of energy balance: chaotic behaviour based on a balance between two unstable “states of charging”, and stable limit cycle behaviour based on the balance between the energy lost in the regions with mainly positive losses and the energy gained in the regions with mainly negative losses. Convergence problems observed in connection with simulation of the ideal piecewise-linear model are solved by means of a smooth continuous model of the nonlinear element based on the ideal operational amplifier model instead of a polynomial approximation. The movements of the eigenvalues as functions of the nonlinear resistance are found. Stable limit cycles of periods 1, 2, 3 and 5 are found by introducing losses",

author = "Erik Lindberg",

note = "Copyright: 1994 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE; 1994 IEEE International Symposium on Circuits and Systems, ISCAS '94 ; Conference date: 30-05-1994 Through 02-06-1994",

year = "1994",

doi = "10.1109/ISCAS.1994.409513",

language = "English",

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booktitle = "Proceedings of the IEEE International Symposium on Circuits and Systems",

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AU - Lindberg, Erik

N1 - Copyright: 1994 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 1994

Y1 - 1994

N2 - Experiments with modelling and simulation of sinusoidal excitation on Chua's circuit are presented. It is demonstrated that the behaviour of the circuit is based on the interaction of two different kinds of energy balance: chaotic behaviour based on a balance between two unstable “states of charging”, and stable limit cycle behaviour based on the balance between the energy lost in the regions with mainly positive losses and the energy gained in the regions with mainly negative losses. Convergence problems observed in connection with simulation of the ideal piecewise-linear model are solved by means of a smooth continuous model of the nonlinear element based on the ideal operational amplifier model instead of a polynomial approximation. The movements of the eigenvalues as functions of the nonlinear resistance are found. Stable limit cycles of periods 1, 2, 3 and 5 are found by introducing losses

AB - Experiments with modelling and simulation of sinusoidal excitation on Chua's circuit are presented. It is demonstrated that the behaviour of the circuit is based on the interaction of two different kinds of energy balance: chaotic behaviour based on a balance between two unstable “states of charging”, and stable limit cycle behaviour based on the balance between the energy lost in the regions with mainly positive losses and the energy gained in the regions with mainly negative losses. Convergence problems observed in connection with simulation of the ideal piecewise-linear model are solved by means of a smooth continuous model of the nonlinear element based on the ideal operational amplifier model instead of a polynomial approximation. The movements of the eigenvalues as functions of the nonlinear resistance are found. Stable limit cycles of periods 1, 2, 3 and 5 are found by introducing losses

U2 - 10.1109/ISCAS.1994.409513

DO - 10.1109/ISCAS.1994.409513

M3 - Article in proceedings

SN - 07-80-31915-X

VL - Volume 6

SP - 5

EP - 8

BT - Proceedings of the IEEE International Symposium on Circuits and Systems

PB - IEEE

T2 - 1994 IEEE International Symposium on Circuits and Systems

Y2 - 30 May 1994 through 2 June 1994

ER -

Sinusoidal excitation on the Chua's circuit simulation of limit cycles and chaos

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