Publication detail

New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure

PETRŽELA, J. GÖTTHANS, T.

Original Title

New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure

English Title

New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure

Type

journal article in Web of Science

Language

en

Original Abstract

This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.

English abstract

This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.

Keywords

analog oscillator; autonomous deterministic system; circuit synthesis; chaos; nonlinear dynamics; strange attractor

Released

22.09.2017

Publisher

MDPI

Location

Basel, Switzerland

ISBN

2076-3417

Periodical

Applied Sciences - Basel

Year of study

7

Number

10

State

CH

Pages from

976

Pages to

988

Pages count

13

URL

Full text in the Digital Library

Documents

BibTex


@article{BUT139701,
  author="Jiří {Petržela} and Tomáš {Götthans}",
  title="New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure",
  annote="This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.",
  address="MDPI",
  chapter="139701",
  doi="10.3390/app7100976",
  howpublished="online",
  institution="MDPI",
  number="10",
  volume="7",
  year="2017",
  month="september",
  pages="976--988",
  publisher="MDPI",
  type="journal article in Web of Science"
}