| Jesus Manuel Muñoz-Pacheco |
| Benemérita Universidad Autónoma de Puebla, Mexico |
Abstract: Fractional-order calculus provides unique characteristics to dynamical systems. For instance, in 3D dynamical systems, their effective dimension, defined as the summation of the involved derivative orders, can be lower than three, but surprisingly, generates chaotic behavior. Thus, the Poincaré-Bedixon theorem does not apply to those fractional-order systems. A fractional-order dynamical system is considered as a generalization of the integer-order versions.
Therefore, several works giving the fractional-order form of well-known chaotic systems
such as Chua’s system, Chen, Lorenz, and others were reported last decade. Also, new chaotic
systems with constant and variable fractional derivatives have been recently proposed.
One of the advantages of fractional-order calculus is that it permits more accurate
mathematical modeling than its integer-order counterpart, especially in real-life applications.
This is due to the extra degrees of freedom that introduce fractional orders as new parameters.
Therefore, they are widely proposed for several engineering applications: encryption,
memristors, robotics, true random number generators, bio-engineering, control systems,
filters, and so forth. Because the core of the applications mentioned above is hardware
capable of reproducing the fractional-order behavior, novel and inexpensive design
approaches are demanded and needed. From an electronics point of view, analog circuit
implementations seek emulators for fractional-order integrators 1 𝑠 !⁄, with 𝛼=fractional-
order, whereas the digital implementations, are majority based on numerical integration
methods.
The lecture presents concise design guidelines for implementing fractional-order systems
using digital platforms and analog electronic devices. New concepts and experimental
circuits that may allow the audience to implement the outlined strategies at low cost are
presented. Finally, we forecast the research opportunities and future challenges in this
exciting scientific area.