Publication detail

A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium

VIET-THANH, P. VOLOS, C. SAJAD, J. GÖTTHANS, T.

Original Title

A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium

Type

book chapter

Language

English

Original Abstract

Recently, Leonov and Kuznetsov have introduced a new definition “hidden attractor”. Systems with hidden attractors, especially chaotic systems, have attracted significant attention. Some examples of such systems are systems with a line equilibrium, systems without equilibrium or systems with stable equilibria etc. In some interesting new research, systems in which equilibrium points are located on different special curves are reported. This chapter introduces a three-dimensional autonomous system with a square-shaped equilibrium and without equilibrium points. Therefore, such system belongs to a class of systems with hidden attractors. The fundamental dynamics properties of such system are studied through phase portraits, Poincaré map, bifurcation diagram, and Lyapunov exponents. Anti-synchronization scheme for our systems is proposed and confirmed by the Lyapunov stability. Moreover, an electronic circuit is implemented to show the feasibility of the mathematical model. Finally, we introduce the fractional order form of such system.

Keywords

Chaos; nonlinear; circuits; Lyapunov exponents

Authors

VIET-THANH, P.; VOLOS, C.; SAJAD, J.; GÖTTHANS, T.

Released

1. 4. 2017

Publisher

Springer, Cham

ISBN

978-3-319-50249-6

Book

Fractional Order Control and Synchronization of Chaotic Systems

Edition

illustrated

Edition number

688

Pages from

613

Pages to

635

Pages count

22

URL

https://link.springer.com/chapter/10.1007%2F978-3-319-50249-6_21

BibTex

@inbook{BUT141115,
  author="Pham {Viet-Thanh} and Christos {Volos} and Jafari {Sajad} and Tomáš {Götthans}",
  title="A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium",
  booktitle="Fractional Order Control and Synchronization of Chaotic Systems",
  year="2017",
  publisher="Springer, Cham",
  series="illustrated",
  edition="688",
  pages="613--635",
  doi="10.1007/978-3-319-50249-6\{_}21",
  isbn="978-3-319-50249-6",
  url="https://link.springer.com/chapter/10.1007%2F978-3-319-50249-6_21"
}