Parametric control on fractional-order response for Lü chaotic system

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

Research output: Contribution to journalArticle

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
Article number012024
JournalJournal of Physics: Conference Series
Volume423
Issue number1
DOIs
Publication statusPublished - 2013

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dynamical systems
degrees of freedom
shift

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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Parametric control on fractional-order response for Lü chaotic system. / Moaddy, K.; Radwan, A. G.; Salama, K. N.; Momani, S.; Hashim, Ishak.

In: Journal of Physics: Conference Series, Vol. 423, No. 1, 012024, 2013.

Research output: Contribution to journalArticle

Moaddy, K. ; Radwan, A. G. ; Salama, K. N. ; Momani, S. ; Hashim, Ishak. / Parametric control on fractional-order response for Lü chaotic system. In: Journal of Physics: Conference Series. 2013 ; Vol. 423, No. 1.
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