ON A CLOSENESS OF THE JULIA SETS OF NOISE-PERTURBED COMPLEX QUADRATIC MAPS-Reference-Cited by-同舟云学术

ON A CLOSENESS OF THE JULIA SETS OF NOISE-PERTURBED COMPLEX QUADRATIC MAPS

Published:2012-09 Issue:09 Volume:22 Page:1250221
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

ANDREADIS IOANNIS¹,KARAKASIDIS THEODOROS E.²

Affiliation:

1. International School of The Hague, Wijndaelerduin 1, 2554 BX The Hague, The Netherlands

2. Department of Civil Engineering, University of Thessaly, GR-38334 Volos, Greece

Abstract

In the present work, we extend the results of the study of the structural stability of the Julia sets of noise-perturbed complex quadratic maps in the presence of dynamic and output noise both for the additive and the multiplicative cases. The critical values of the strength of the noise for which the Julia set of a family of noise-perturbed complex quadratic maps completely loses its original Julia structure were also calculated. Using graphical tools we demonstrate how one can localize the regions of the Julia sets that are affected by the presence of noise in each case. Finally, two numerical invariants for the Julia set of noise-perturbed complex quadratic maps are proposed for the study of the noise effect.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127412502215

Reference22 articles.

1. On probabilistic Mandelbrot maps

2. The influence of noise on the correlation dimension of chaotic attractors

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