Publication detail

A chaotic system with rounded square equilibrium and with no-equilibrium

VIET-THANH, P. SAJAD, J. VOLOS, C. GÖTTHANS, T. WANG, X. VO HOANG, D.

Original Title

A chaotic system with rounded square equilibrium and with no-equilibrium

English Title

A chaotic system with rounded square equilibrium and with no-equilibrium

Type

journal article in Web of Science

Language

en

Original Abstract

Chaotic systems with an infinite number of equilibrium points and chaotic ones without equilibrium have received a significant attention in the last years because they belong to a class of systems with “hidden attractor”. In this work, we introduce a three-dimensional chaotic system displaying both hidden attractors with infinite equilibria and hidden attractors without equilibrium. Surprisingly, when the system exhibits hidden attractors with infinite equilibria, it has a rounded square curve of equilibrium points. Dynamical properties of the new system are analyzed through equilibrium points, phase portraits, bifurcation diagram, and maximal Lyapunov exponents. Furthermore, circuit implementation of the system is presented showing another approach to study such system as well as its feasibility.

English abstract

Chaotic systems with an infinite number of equilibrium points and chaotic ones without equilibrium have received a significant attention in the last years because they belong to a class of systems with “hidden attractor”. In this work, we introduce a three-dimensional chaotic system displaying both hidden attractors with infinite equilibria and hidden attractors without equilibrium. Surprisingly, when the system exhibits hidden attractors with infinite equilibria, it has a rounded square curve of equilibrium points. Dynamical properties of the new system are analyzed through equilibrium points, phase portraits, bifurcation diagram, and maximal Lyapunov exponents. Furthermore, circuit implementation of the system is presented showing another approach to study such system as well as its feasibility.

Keywords

Chaos; Hidden attractor; Equilibrium; Electronic circuit

Released

03.11.2016

Publisher

Elsevier GmbH

ISBN

0030-4026

Periodical

OPTIK

Year of study

127

Number

4

State

DE

Pages from

1

Pages to

7

Pages count

7

Documents

BibTex


@article{BUT129430,
  author="Viet-Thanh {Pham} and Jafari {Sajad} and Christos {Volos} and Tomáš {Götthans} and Xiong {Wang} and Duy {Vo Hoang}",
  title="A chaotic system with rounded square equilibrium and with no-equilibrium",
  annote="Chaotic systems with an infinite number of equilibrium points and chaotic ones without equilibrium have received a significant attention in the last years because they belong to a class of systems with “hidden attractor”. In this work, we introduce a three-dimensional chaotic system displaying both hidden attractors with infinite equilibria and hidden attractors without equilibrium. Surprisingly, when the system exhibits hidden attractors with infinite equilibria, it has a rounded square curve of equilibrium points. Dynamical properties of the new system are analyzed through equilibrium points, phase portraits, bifurcation diagram, and maximal Lyapunov exponents. Furthermore, circuit implementation of the system is presented showing another approach to study such system as well as its feasibility.",
  address="Elsevier GmbH",
  chapter="129430",
  doi="10.1016/j.ijleo.2016.10.100",
  howpublished="online",
  institution="Elsevier GmbH",
  number="4",
  volume="127",
  year="2016",
  month="november",
  pages="1--7",
  publisher="Elsevier GmbH",
  type="journal article in Web of Science"
}