CONTROL AND SYNCHRONIZATION OF JULIA SETS GENERATED BY A CLASS OF COMPLEX TIME-DELAY RATIONAL MAP

被引：5
作者：
Wang, Da [1 ]
Liu, Shutang [1 ]
Liu, Kexin [2 ]
Zhao, Yang [1 ]
机构：
[1] Shandong Univ, Coll Control Sci & Engn, Jinan 250061, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100191, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2016年 / 6卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Time-delay complex system; julia set; control; synchronization; GENERALIZED MANDELBROT SETS; TOPOLOGICAL CLOSENESS; DYNAMICAL-SYSTEMS; FRACTAL STRUCTURE; NOISE; CHAOS;
D O I：
10.11948/201A68
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a class of complex time-delay rational map is studied by analyzing the fractal and dynamical properties of its corresponding Julia sets (CTRM-Julia sets for short). By utilizing these given properties, a hybrid control method which contains both state feedback and parameters perturbation is applied to achieve the boundary control of CTRM-Julia set. Moreover, the synchronization of two different CTRM-Julia sets is also investigated by using coupling method. The synchronization index method is applied to demonstrate the relationship between the degree of synchronization and the coupling strength. Numerical examples are given to verify the effectiveness of control and synchronization methods.
引用
收藏
页码：1049 / 1063
页数：15
相关论文
共 42 条
[1]   On numerical approximations of the area of the generalized Mandelbrot sets [J].
Andreadis, Ioannis ;
Karakasidis, Theodoros E. .
APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (23) :10974-10982
[2]   ON A CLOSENESS OF THE JULIA SETS OF NOISE-PERTURBED COMPLEX QUADRATIC MAPS [J].
Andreadis, Ioannis ;
Karakasidis, Theodoros E. .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (09)
[3]   On a topological closeness of perturbed Julia sets [J].
Andreadis, Ioannis ;
Karakasidis, Theodoros E. .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (06) :2883-2890
[4]   On a topological closeness of perturbed Mandelbrot sets [J].
Andreadis, Ioannis ;
Karakasidis, Theodoros E. .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (10) :3674-3683
[5]   On probabilistic Mandelbrot maps [J].
Andreadis, Ioannis ;
Karakasidis, Theodoros E. .
CHAOS SOLITONS & FRACTALS, 2009, 42 (03) :1577-1583
[6]  
[Anonymous], 2004, GRAPHICS MATH FRACTA
[7]   On the Julia set of the perturbed Mandelbrot map [J].
Argyris, J ;
Karakasidis, TE ;
Andreadis, I .
CHAOS SOLITONS & FRACTALS, 2000, 11 (13) :2067-2073
[8]   On perturbations of the Mandelbrot map [J].
Argyris, J ;
Andreadis, I ;
Karakasidis, TE .
CHAOS SOLITONS & FRACTALS, 2000, 11 (07) :1131-1136
[9]   On the Julia sets of a noise-perturbed Mandelbrot map [J].
Argyris, J ;
Karakasidis, TE ;
Andreadis, I .
CHAOS SOLITONS & FRACTALS, 2002, 13 (02) :245-252
[10]   Physical meaning for Mandelbrot and Julia sets [J].
Beck, C .
PHYSICA D, 1999, 125 (3-4) :171-182
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