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Moaddy, K.; Hashim, I.; Momani, S.

Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems. (English) Zbl 1228.65119

Comput. Math. Appl. 62, No. 3, 1068-1074 (2011).
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.

Cited in 12 Documents

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34C28 Complex behavior and chaotic systems of ordinary differential equations
45J05 Integro-ordinary differential equations

Keywords:

fractional differential equations; chaos; non-standard finite deference schemes; Rössler system
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\textit{K. Moaddy} et al., Comput. Math. Appl. 62, No. 3, 1068--1074 (2011; Zbl 1228.65119)
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