Parametric Control on Fractional-Order Response for Lü Chaotic System

K Moaddy, A G Radwan, Khaled N. Salama, S Momani, I Hashim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.
Original languageEnglish (US)
Title of host publicationJournal of Physics: Conference Series
PublisherIOP Publishing
Pages012024
DOIs
StatePublished - Apr 10 2013

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