Publication detail
Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment
PETRŽELA, J., HANUS, S., KOLKA, Z.
Original Title
Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment
English Title
Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment
Type
journal article - other
Language
en
Original Abstract
This paper shows the circuitry implementation and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots.
English abstract
This paper shows the circuitry implementation and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots.
Keywords
Nonlinear oscillator, chaos, Lyapunov exponents, circuit realization, measurement
RIV year
2006
Released
25.03.2006
ISBN
1210-2512
Periodical
Radioengineering
Year of study
15
Number
1
State
CZ
Pages from
6
Pages to
11
Pages count
6
Documents
BibTex
@article{BUT46676,
author="Jiří {Petržela} and Stanislav {Hanus} and Zdeněk {Kolka}",
title="Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment",
annote="This paper shows the circuitry implementation
and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have
direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element
were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots.",
chapter="46676",
journal="Radioengineering",
number="1",
volume="15",
year="2006",
month="march",
pages="6--11",
type="journal article - other"
}