FPGA implementation of two fractional order chaotic systems

• Published in: International journal of electronics and communications 2017-08, Vol.78, p.162-172
• Main Authors: Tolba, Mohammed F., AbdelAty, Amr M., Soliman, Nancy S., Said, Lobna A., Madian, Ahmed H., Azar, Ahmad Taher, Radwan, Ahmed G.
• Format: Article
• Language: English
• Subjects: Chaotic systems; FPGA; Fractional order; Liu system; Multi-scroll; V-Shape
• ISSN: 1434-8411; 1618-0399
• DOI: 10.1016/j.aeue.2017.04.028

This paper discusses the FPGA implementation of the fractional-order derivative as well as two fractional-order chaotic systems where one of them has controllable multi-scroll attractors. The complete hardware architecture of the Grünwald-Letnikov (GL) differ-integral is realized with different memory window sizes. As an application of the proposed circuit, a complete fractional-order FPGA implementation of Liu chaotic system is introduced with different fractional-orders. Moreover, a fractional-order controllable heart and V-shape multi-scrolls chaotic systems are verified in the case of symmetric and asymmetric cases. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional-orders. To verify the chaotic behavior of many generating attractors, the Maximum Lyapunov Exponent (MLE) is calculated for such systems. The designs have been simulated using Xilinx ISE 14.5 and realized on Xilinx FPGA Virtex 5 XC5VLX50T. The achieved throughputs are: 4.4Gbit/s for GL, 1.986Gbit/s for Liu system, and 2.921Gbit/s for V-Shape multi-scroll attractor.