Stability, Synchronization Control and Numerical Solution of Fractional Shimizu–Morioka Dynamical System

Authors

Mehmet Ali Akinlar, Yildiz Technical University, Faculty of Chemical and Metallurgical Engineering, Department of Mathematical Engineering, 34210- Davutpasa-Istanbul, Turkey
Aydin Secer
Mustafa Bayram

Author Country (or Countries)

Turkey

Abstract

In this paper we concern with asymptotic stability, synchronization control and numerical solution of incommensurate order fractional Shimizu–Morioka dynamical system. Firstly we prove the existence and uniqueness of the solutions via a new theorem. After finding steady–state points, we obtain necessary and sufficient conditions for the asymptotic stability of the Shimizu–Morioka system.We also study the synchronization control where we employ master–slave synchronization scheme. Finally, employing Adams– Bashforth–Moulton’s technique we solve the Shimizu–Morioka system numerically. To the best of our knowledge, there exist not any study about analysis of chaotic dynamics of fractional Shimizu–Morioka system in the literature. In this sense the present paper is going to be a totally new contribution and highly useful research for synthesis of a nonlinear system of fractional equations.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/080426

Recommended Citation

Ali Akinlar, Mehmet; Secer, Aydin; and Bayram, Mustafa (2014) "Stability, Synchronization Control and Numerical Solution of Fractional Shimizu–Morioka Dynamical System," Applied Mathematics & Information Sciences: Vol. 08: Iss. 4, Article 26.
DOI: http://dx.doi.org/10.12785/amis/080426
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss4/26