SOME COMPLEX DYNAMICAL BEHAVIORS OF THE NEW 6D FRACTIONAL-ORDER HYPERCHAOTIC LORENZ-LIKE SYSTEM | Zendy

Ahmed A. Farghaly | Zendy; A.A.-H. Shoreh | Zendy

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SOME COMPLEX DYNAMICAL BEHAVIORS OF THE NEW 6D FRACTIONAL-ORDER HYPERCHAOTIC LORENZ-LIKE SYSTEM

Author(s) -

Ahmed A. Farghaly,

A.A.-H. Shoreh

Publication year - 2018

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.21608/jomes.2018.9469

Subject(s) - mathematics , order (exchange) , control theory (sociology) , computer science , artificial intelligence , control (management) , economics , finance

In this paper, we introduce the fractional version of the new 6D hyperchaotic Lorenz-likesystem which has been introduced recently in the literature. Hyperchaotic behaviors of higherorder increase the randomness and higher unpredictability of the corresponding system. Somecomplex dynamical behaviors such as hyperchaotic of order 5, Poincare mapping and bifurcationdiagram are analyzed and investigated. The stability region of the new fractional-ordersystem is investigated. The values of the fractional-order and the system parameters at whichhyperchaotic attractors exist are calculated based on the sign of their Lyapunov exponents.The complete synchronization of the hyperchaotic attractors of order 5 is studied. A scheme isstated to derive the analytical formula of the control function to study this kind of synchronization.An excellent agreement is found upon comparison this analytical formula with numericalexperiments.

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