Two‐Dimensional Discrete Dynamical Systems – Oxford Scholarship

Chapter:

(p.272) (p.273) Two‐Dimensional Discrete Dynamical Systems

Source:

Chaos and Fractals

Author(s):

David P. Feldman

Writer:

Oxford College Press

DOI:10.1093/acprof:oso/9780199566433.003.0027

Dynamical systems could be iterated functions of 1 continuous variable. A good example of this type of product is the iterated logistic equation. This chapter concentrates on two-dimensional discrete dynamical systems. It first provides an introduction to one-dimensional dynamical systems, a canonical example being the logistic equation, f(x) = rx(1 – x), where x may take any value between and 1. After that it examines the lengthy-term behavior of orbits, whether you will find fixed points, whether initial conditions tend toward infinity, if the orbits are chaotic, and whether there’s sensitive reliance on initial conditions. These questions are addressed utilizing a dynamical system referred to as Hénon map. The chapter also explains how you can represent and consider periodic conduct for any two-dimensional iterated function and describes strange attractors, a good example to be the Hénon attractor.

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