Self-affine Fractals Generated by Nonlinear Systems
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.
KeywordsIterate Function System Spectral Norm Linear Factor Fractal Attractor Choose Point
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- 3.Kocić, L.M., Simoncelli, A.C.: Shape predictable IFS representations. In: Novak, M.M. (ed.) Emergent Nature, pp. 435–436. World Scientific, Singapore (2002)Google Scholar
- 4.Kocić, L.M., Gegovska-Zajkova, S., Babače, E.: Nonlinear systems and iterated function system, Differential geometry - Dynamical Systems. In: Balkan Society of geometers, vol. 10, pp. 197–205, M.S.C. 2000: 34A34, 28A80. Geometry Balkan Press (2008)Google Scholar