Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

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",
  annote="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.",
  address="Springer, Cham",
  booktitle="Fractional Order Control and Synchronization of Chaotic Systems",
  chapter="141115",
  doi="10.1007/978-3-319-50249-6_21",
  edition="illustrated",
  howpublished="print",
  institution="Springer, Cham",
  year="2017",
  month="april",
  pages="613--635",
  publisher="Springer, Cham",
  type="book chapter"
}