Further analytical bifurcation analysis and applications of coupled logistic maps

被引:28
作者
Elsadany, A. A. [1 ,2 ]
Yousef, A. M. [3 ]
Elsonbaty, Amr [4 ]
机构
[1] Prince Sattam Bin Abdulaziz Univ, Math Dept, Coll Sci & Humanities Studies Al Kharj, Al Kharj, Saudi Arabia
[2] Suez Canal Univ, Fac Comp & Informat, Basic Sci Dept, Ismailia 41522, Egypt
[3] South Valley Univ, Fac Sci, Qena, Egypt
[4] Mansoura Univ, Fac Engn, Math & Engn Phys Dept, PO 35516, Mansoura, Egypt
关键词
Neimark-Sacker bifuraction; Marotto's chaos; Image encryption; Coupled logistic map; SYNCHRONIZED CHAOS; SIMPLE-MODEL; ENCRYPTION; SCHEME; HETEROGENEITY; DYNAMICS; STANDARD; ARRAYS;
D O I
10.1016/j.amc.2018.06.008
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, we extend further the analytical study of complex dynamics exist in two coupled logistic maps. New results about the occurrence of various types of bifurcation in the system, including flip bifurcation, pitchfork bifurcation and Neimark-Sacker bifurcation are presented. To the best of authors' knowledge, the presence of chaotic dynamics in system's behavior has been investigated and proved analytically via Marotto's approach for first time. Numerical simulations are carried out in order to verify theoretical results. Furthermore, chaos based encryption algorithm for images is presented as an application for the coupled logistic maps. Different scenarios of attacks are considered to demonstrate its immunity and effectiveness against the possible attacks. Finally, a circuit realization for the coupled logistic maps is proposed and utilized in a suggested real time text encryption system. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码:314 / 336
页数:23
相关论文
共 63 条
  • [1] Alligood K. T., 1996, CHAOS
  • [2] [Anonymous], 2002, LINKED EVERYTHING IS
  • [3] [Anonymous], 2008, Dynamical Processes on Complex Networks
  • [4] [Anonymous], 2009, ITERATED MAPS INTERV
  • [5] Askar S. S., 2015, MATH PROBL ENG, DOI [10.1155/7015/11109, DOI 10.1155/7015/11109]
  • [6] Dynamics of the kicked logistic map
    Baptista, MS
    Caldas, IL
    [J]. CHAOS SOLITONS & FRACTALS, 1996, 7 (03) : 325 - 336
  • [7] The parameter space structure of the kicked logistic map and its stability
    Baptista, MS
    Caldas, IL
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1997, 7 (02): : 447 - 457
  • [8] Borujeni S.E., 2015, APPL MATH, V6, P773, DOI [10.4236/am.2015.65073, DOI 10.4236/am.2015.65073]
  • [9] A family of multimodal dynamic maps
    Campos-Canton, E.
    Femat, R.
    Pisarchik, A. N.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (09) : 3457 - 3462
  • [10] Improvement of trace-driven I-Cache timing attack on the RSA algorithm
    Chen, CaiSen
    Wang, Tao
    Kou, YingZhan
    Chen, XiaoCen
    Li, Xiong
    [J]. JOURNAL OF SYSTEMS AND SOFTWARE, 2013, 86 (01) : 100 - 107