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

Pages from

6

Pages to

11

Pages count

6

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"
}