Fractional-order Complex Chaotic Systems: FPGA Implementation and Applications

Research Project

Fractional calculus (FC) has been proved through numerous research examples to be a superior tool for system description to the narrow integer order domain. This is achieved through the extra parameters introduced by allowing the differential or integral orders to take non-integer values. The promising capabilities of fractional-order devices challenge the research to find a way to simulate its behaviour until its off-shelf appearance. Different integer-order approximation techniques to the fractional-order transfer functions are investigated in the literature. There are many categories of fractional-order system approximations in analogue and digital domains, which will be investigated in this project.

Fractional-order systems are difficult to translate into hardware as their memory dependency requires the use of high-order integer systems. FPGA technology is quite suitable for implementing complex systems. Designers are increasingly relied on the reuse of IP (Intellectual Property) cores to reduce their production cycle time and development cost. From a digital point of view, this project integrates the programmable IP core with any application and implements it in a system-on-chip (SOC) configuration. The architecture of the IP core is quite flexible and simple to integrate with the targeted applications.



The contribution of this work is the development of a methodology which provides practical and efficient ways to implement fractional-order systems with:

  • Designing and developing an FPGA IP core that can be used for reconfigurable fractional-order chaotic systems.
  • Implementing chaotic systems with transcendental functions using effective methods such as CORDIC.
  • Designing and realizing fractals based on complex chaotic maps.
  • Using the implemented systems in various applications like image enhancement, image encryption and multi-scroll generation.


Outcome: Publications

  • Elnawawy, M., Aloul, F., Sagahyroon, A., Elwakil, A. S., Sayed, W. S., Said, L. A., Mohamed, S. M., Radwan, A. G. (2021). FPGA Realizations of Chaotic Epidemic and Disease Models Including Covid-19. IEEE Access9, 21085-21093.‏
  •  Mohamed, S. M., Sayed, W. S., Said, L. A., & Radwan, A. G. (2021). Reconfigurable FPGA Realization of Fractional-Order Chaotic Systems. IEEE Access9, 89376-89389.