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

Research output

Abstract

In this paper, we introduce the fractional version of the new 6D hyperchaotic Lorenz-like
system which has been introduced recently in the literature. Hyperchaotic behaviors of higher
order increase the randomness and higher unpredictability of the corresponding system. Some
complex dynamical behaviors such as hyperchaotic of order 5, Poincare mapping and bifurcation
diagram are analyzed and investigated. The stability region of the new fractional-order
system is investigated. The values of the fractional-order and the system parameters at which
hyperchaotic 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 is
stated 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 numerical
experiments.
Original languageEnglish
Pages (from-to)138-155
Number of pages18
JournalJournal of the Egyptian Mathematical Society
Volume26
Issue number1
DOIs
Publication statusPublished - 2018

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