Characterization of a Family of Cubic Dynamical Systems

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Authors
Kothari, Shan
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Issue Date
2011
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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.