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

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Akınlar M. A. , Seçer A., Bayram M.

APPLIED MATHEMATICS & INFORMATION SCIENCES, vol.8, pp.1699-1705, 2014 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8
  • Publication Date: 2014
  • Doi Number: 10.12785/amis/080426
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1699-1705
  • Keywords: Fractional Shimizu-Morioka equation, stability, synchronization control, numerical solution, Adams-Bashforth-Moulton method, Caputo fractional derivative, DIFFERENTIAL SYSTEM, CHAOTIC SYSTEMS


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.