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Zbl 1228.65119
Moaddy, K.; Hashim, I.; Momani, S.
Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems. (English)
[J] Comput. Math. Appl. 62, No. 3, 1068-1074 (2011). ISSN 0898-1221

Summary: The non-standard finite difference method (for short NSFD) is implemented to study the dynamic behaviors in the fractional-order Rössler chaotic and hyperchaotic systems. The Grünwald-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 Rössler 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.

MSC 2000:: *65L12 Finite difference methods for ODE
37D45 Strange attractors, chaotic dynamics
34A08
26A33 Fractional derivatives and integrals (real functions)
34C28 Other types of "recurrent" solutions of ODE
45J05 Integro-ordinary differential equations

Keywords: fractional differential equations; chaos; non-standard finite deference schemes; Rössler system

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Zentralblatt MATH Berlin [Germany]