Complex Dynamics of the Fractional-Order Rössler System and Its Tracking Synchronization Control

• Published in: Complexity (New York, N.Y.) Vol. 2018; no. 2018; pp. 1 - 13
• Main Authors: Wang, Huihai, Sun, Kehui, He, Shaobo
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01-01-2018; Hindawi; John Wiley & Sons, Inc; Hindawi Limited; Hindawi-Wiley
• Subjects: Algorithms; Analysis; Applied mathematics; Bifurcations; Chaos theory; Cybernetics; Decomposition; Iterative methods; Neural networks; Numerical analysis; Order parameters; Phase diagrams; Physics; Synchronism; Tracking control
• ISSN: 1076-2787; 1099-0526
• DOI: 10.1155/2018/4019749

Numerical analysis of fractional-order chaotic systems is a hot topic of recent years. The fractional-order Rössler system is solved by a fast discrete iteration which is obtained from the Adomian decomposition method (ADM) and it is implemented on the DSP board. Complex dynamics of the fractional-order chaotic system are analyzed by means of Lyapunov exponent spectra, bifurcation diagrams, and phase diagrams. It shows that the system has rich dynamics with system parameters and the derivative order q. Moreover, tracking synchronization controllers are theoretically designed and numerically investigated. The system can track different signals including chaotic signals from the fractional-order master system and constant signals. It lays a foundation for the application of the fractional-order Rössler system.