CHAOTIC DYNAMICAL SYSTEMS AND THEIR APPLICATIONS

J. CORDOVA ZECEÑA

University of Arkansas
Department of Computer Science and Computer Engineering
Engineering Hall 3112
Fayetteville, Arkansas 72701

Abstract:

In this paper we deal with chaotic dynamical systems and their use in solving practical problems like estimating the future of a system and affecting secure information exchange. We discuss the general characteristics of dynamical systems and how these arise, partly, through a combination of unstable fixed points and period doubling bifurcations induced on equilibrium points through the varying of a parameter. We see how some of these characteristics are common to all dynamical systems of a generalized class (systems with local quadratic maxima) and allow, therefore, for abstraction and exact calculation independent of the particular system being studied. Finally, we propose specific methods to implement an efficient cryptographic system and a signal prediction scheme.