Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems

Authors:
K. Moaddy;I. Hashim;S. Momani
Affiliations:
School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia;School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia;Department of Mathematics, The University of Jordan, Amman 11942, Jordan
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, the non-standard finite difference method (for short NSFD) is implemented to study the dynamic behaviors in the fractional-order Rossler chaotic and hyperchaotic systems. The Grunwald-Letnikov method is used to approximate the fractional derivatives. We found that the lowest value to have chaos in this system is 2.1 and hyperchaos exists in the fractional-order Rossler system of order as low as 3.8. Numerical results show that the NSFD approach is easy to implement and accurate when applied to differential equations of fractional order.