Self-affine Fractals Generated by Nonlinear Systems

  • Authors:

  • Ljubiša Kocić;Sonja Gegovska-Zajkova;Elena Babače

  • Affiliations:

  • Faculty of Electronic Engineering, University of Niš, Niš, Serbia 18 000;Faculty of Electrical Engineering and Information Technologies, Ss Cyril and Methodius University, Skopje, R.Macedonia;Faculty of Electrical Engineering and Information Technologies, Ss Cyril and Methodius University, Skopje, R.Macedonia

  • Venue:
  • Numerical Analysis and Its Applications
  • Year:
  • 2009

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Abstract

A system of ODE's with nonlinear terms exhibits a nonlinear dynamic behavior. Under some conditions these terms can be locally approximated by linear factors, which can be, after discretization transformed in the sequence of (hyperbolic) Iterated Function Systems (IFS) that generates a unique fractal attractor. This attractor reflects the dynamics in the vicinity of the approximated point of the nonlinear system. Here, the IFS is replaced with an associate AIFS (Affine invariant IFS), a kind of IFS that has affine invariance property and permits further manipulating of this fractal attractor.