Characterization of a Family of Cubic Dynamical Systems

Abstract

Motivated by the fact that cubic maps have found potential appli- cations to modeling of biological and physical processes, we examine a family of discrete, non-linear dynamical systems comprising one-parameter real variable cubic polynomials of a certain form. We examine and classify their ����xed points and 2-cycles over various parametric domains. We also study their bifurcation diagrams and use a variety of techniques to analyze their chaotic behavior.