Arbitrary-Order Calculus and its Emerging Applications.

Ponente(s): Carlos Sánchez López

This talk addresses the topic of deterministic chaos modeled by differential equations of integer and arbitrary order. It describes some natural and mechanical phenomena with chaotic behavior, before focusing on the modeling and simulation of such dynamic systems. Numerical methods for solving differential equations of arbitrary order are discussed, as well as how to use rational approximations of integer order to approximate arbitrary order. In the second part, some emerging applications of chaos theory in robotics, data encryption, and secure communications are described. Preliminary experimental evidence using reconfigurable hardware is presented for some of these applications.