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Erschienen in:
Comparative Study on Fractional Order PID and PID Controllers on Noise Suppression for Manipulator Trajectory Control Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

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

verfasst von : Viet-Thanh Pham, Sundarapandian Vaidyanathan, Christos K. Volos, Sajad Jafari, Tomas Gotthans

Erschienen in: Fractional Order Control and Synchronization of Chaotic Systems

Verlag: Springer International Publishing

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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.

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Vorheriges Kapitel A New Method to Synchronize Fractional Chaotic Systems with Different Dimensions
Nächstes Kapitel A Study on Coexistence of Different Types of Synchronization Between Different Dimensional Fractional Chaotic Systems
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Metadaten
Titel
A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium
verfasst von
Viet-Thanh Pham
Sundarapandian Vaidyanathan
Christos K. Volos
Sajad Jafari
Tomas Gotthans
Copyright-Jahr
2017
Buch
Fractional Order Control and Synchronization of Chaotic Systems

Print ISBN: 978-3-319-50248-9

Electronic ISBN: 978-3-319-50249-6

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-50249-6_21