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

被引：13

作者：

Andreadis, Ioannis ^{[1
]}

Karakasidis, Theodoros E. ^{[2
]}

机构：

[1] Int Sch The Hague, NL-2554 BX The Hague, Netherlands

[2] Univ Thessaly, Dept Civil Engn, GR-38334 Volos, Greece

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 09期

关键词：

Julia set; complex quadratic map; noise-perturbed complex quadratic map; deviation distance; MANDELBROT SETS; TOPOLOGICAL CLOSENESS;

D O I：

10.1142/S0218127412502215

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：14

共 22 条

[1] On a topological closeness of perturbed Julia sets [J].

Andreadis, Ioannis ;

Karakasidis, Theodoros E. .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (06) :2883-2890

[2] On a topological closeness of perturbed Mandelbrot sets [J].

Andreadis, Ioannis ;

Karakasidis, Theodoros E. .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (10) :3674-3683

[3] On probabilistic Mandelbrot maps [J].

Andreadis, Ioannis ;

Karakasidis, Theodoros E. .

CHAOS SOLITONS & FRACTALS, 2009, 42 (03) :1577-1583

[4]

[Anonymous], 1986, The beauty of fractals: images of complex dynamical systems

[5] On the Julia set of the perturbed Mandelbrot map [J].

Argyris, J ;

Karakasidis, TE ;

Andreadis, I .

CHAOS SOLITONS & FRACTALS, 2000, 11 (13) :2067-2073

[6] The influence of noise on the correlation dimension of chaotic attractors [J].

Argyris, J ;

Andreadis, I ;

Pavlos, G ;

Athanasiou, M .

CHAOS SOLITONS & FRACTALS, 1998, 9 (03) :343-361

[7] On perturbations of the Mandelbrot map [J].

Argyris, J ;

Andreadis, I ;

Karakasidis, TE .

CHAOS SOLITONS & FRACTALS, 2000, 11 (07) :1131-1136

[8]

Argyris J., 1994, EXPLORATION CHAOS

[9]

Barnsley M.F., 2006, Superfractals

[10]

Dieudonne J., 1969, ELEMENTS ANAL

← 1 2 3 →