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Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems. (English) Zbl 1228.65119
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:
 65L12 Finite difference methods for ODE (numerical methods) 37D45 Strange attractors, chaotic dynamics 34A08 Fractional differential equations 26A33 Fractional derivatives and integrals (real functions) 34C28 Complex behavior, chaotic systems (ODE) 45J05 Integro-ordinary differential equations
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