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

摘要

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 Griinwald-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.