广义二维多项式混沌映射及其在信息传输中的应用

闫文浩; 姜子敬; 黄欣; 朱淑娟; 丁群

doi:10.11959/j.issn.1000-436x.2022168

您当前的位置：

首页 >

文章列表页 >

广义二维多项式混沌映射及其在信息传输中的应用

学术论文 | 更新时间：2024-06-05

- 广义二维多项式混沌映射及其在信息传输中的应用
- Generalized 2D polynomial chaotic map and its application in information transmission
- 通信学报 2022年43卷第9期页码：80-89
- 作者机构：
  
  1. 黑龙江大学电子工程学院，黑龙江哈尔滨 150080
  2. 澳大利亚佛林德斯大学科学与工程学院，通斯利 SA 5042
- 作者简介：
  
  [ "闫文浩（1995- ），男，陕西渭南人，黑龙江大学博士生，主要研究方向为混沌映射动力学分析、混沌同步及混沌信息传输" ]
  [ "姜子敬（1994- ），男，黑龙江哈尔滨人，黑龙江大学博士生，主要研究方向为网络信息安全及硬件加密侧信道分析" ]
  [ "黄欣（1992- ），女，黑龙江哈尔滨人，黑龙江大学博士生，主要研究方向为图像加密及网络信息安全" ]
  [ "朱淑娟（1965– ），女，博士，澳大利亚佛林德大学科学与工程学院研究员，主要研究方向为智能计算、数据挖掘、数字水印及信息隐藏" ]
  [ "丁群（1957- ），女，黑龙江哈尔滨人，博士，黑龙江大学教授、博士生导师，主要研究方向为混沌加密算法与系统集成、混沌信息传输和网络信息安全等" ]
- 基金信息：
  
  国家自然科学基金资助项目(61471158);黑龙江省自然科学基金优秀青年基金资助项目(YQ2020F012)
- DOI：10.11959/j.issn.1000-436x.2022168
  中图分类号： TN918
- 网络出版日期：2022-09，
  
  纸质出版日期：2022-09-25
- 稿件说明：
移动端阅览
闫文浩, 姜子敬, 黄欣, 等. 广义二维多项式混沌映射及其在信息传输中的应用[J]. 通信学报, 2022,43(9):80-89.

Wenhao YAN, Zijing JIANG, Xin HUANG, et al. Generalized 2D polynomial chaotic map and its application in information transmission[J]. Journal on communications, 2022, 43(9): 80-89.
闫文浩, 姜子敬, 黄欣, 等. 广义二维多项式混沌映射及其在信息传输中的应用[J]. 通信学报, 2022,43(9):80-89. DOI： 10.11959/j.issn.1000-436x.2022168.

Wenhao YAN, Zijing JIANG, Xin HUANG, et al. Generalized 2D polynomial chaotic map and its application in information transmission[J]. Journal on communications, 2022, 43(9): 80-89. DOI： 10.11959/j.issn.1000-436x.2022168.

摘要

现有混沌映射在工程应用中存在许多缺陷，如混沌参数范围不连续、弱混沌、混沌序列输出不均匀和动力学退化等。基于此，提出了一种广义二维多项式混沌映射，通过设定不同控制参数和多项式最高次数，得到一系列特定 Lyapunov 指数的二维多项式混沌映射。为避免该映射第二个状态方程的输出塌陷为一个固定值，引入了一个不随时间变化的随机扰动变量。然后，通过具体的数值实例验证了该映射的有效性，动力分析表明该映射具有复杂的动力学行为。最后，将该映射应用于信息传输技术，相较于其他混沌映射，该映射可以取得更小的误码率，表明该混沌映射更适用于混沌信息传输。

Abstract

Existing chaotic systems have many defects in engineering applications

such as discontinuous chaotic parameter range

weak chaos

uneven output of chaotic sequences and dynamic degradation.Therefore

a generalized 2D polynomial chaotic mapping model was proposed.By setting different control parameters and the highest degree of polynomial

a series of 2D robust chaotic maps with specific Lyapunov exponent could be obtained.In order to avoid the output of the second state equation collapsing to a fixed value

a random disturbance variable which did not change with time was introduced.Finally

a numerical example was given to verify the effectiveness of the proposed model

and the dynamic analysis showed that the mapping has complex dynamic behavior.Finally

the system was applied to information transmission technology.Compared with other chaotic maps

the system can achieve lower bit error rate

which indicates that the chaotic map is more suitable for chaotic information transmission.

关键词

Keywords

references

VAIDYANATHAN S , VOLOS C ． Advances and applications in chaotic systems ［M］． Berlin : Springer International Publishing , 2016 ．

BURT P M S , DE MORAIS G J H ． Efficient computation of bilinear approximations and Volterra models of nonlinear systems ［J］． IEEE Transactions on Signal Processing , 2018 , 66 ( 3 ): 804 - 816 ．

黄润生 , 黄浩．混沌及其应用:第二版［M］．武汉 : 武汉大学出版社 , 2005 ．

HUANG R S , HUANG H ． Chaos and its application ［M］． 2nd ed ． Wuhan : Wuhan University Press , 2005 ．

HIRSCH M W , SMALE S , DEVANEY R L ． Differential equations,dynamical systems,and an introduction to chaos ［M］． Amsterdam : Elsevier , 2013 ．

SCHUSTER H G , JUST W ． Deterministic chaos ［M］． Berlin : Wiley-VCH , 2005 ．

GUREVICH A , COHEN K , ZHAO Q ． Sequential anomaly detection under a nonlinear system cost ［J］． IEEE Transactions on Signal Processing , 2019 , 67 ( 14 ): 3689 - 3703 ．

WANG Z P , WU H N ． On fuzzy sampled-data control of chaoticsystems via a time-dependent Lyapunov functional approach ［J］． IEEE Transactionson Cybernetics , 2015 , 45 ( 4 ): 819 - 829 ．

JANAKIRAMAN S , THENMOZHI K , RAYAPPAN J B B , et al ． Lightweight chaotic image encryption algorithm for real-time embedded system:implementation and analysis on 32-bit microcontroller ［J］． Microprocessors and Microsystems , 2018 , 56 : 1 - 12 ．

CAO Z L , WANG L D ． A secure video watermarking technique based on hyperchaotic Lorentz system ［J］． Multimedia Tools and Applications , 2019 , 78 ( 18 ): 26089 - 26109 ．

HUA Z Y , ZHOU Y C ． Dynamic parameter-control chaotic system ［J］． IEEE Transactions on Cybernetics , 2016 , 46 ( 12 ): 3330 - 3341 ．

LIU L F , LIU B C , HU H P , et al ． Reducing the dynamical degradation by Bi-coupling digital chaotic maps ［J］． International Journal of Bifurcation and Chaos , 2018 , 28 ( 5 ): 1850059 ．

LI H Z , HUA Z Y , BAO H , et al ． Two-dimensional memristive hyperchaotic maps and application in secure communication ［J］． IEEE Transactions on Industrial Electronics , 2021 , 68 ( 10 ): 9931 - 9940 ．

ZHOU Y C , BAO L , CHEN C L P ． Image encryption using a new parametric switching chaotic system ［J］． Signal Processing , 2013 , 93 ( 11 ): 3039 - 3052 ．

HUA Z Y , ZHOU Y C , PUN C M , et al ． 2D sine logistic modulation map for image encryption ［J］． Information Sciences , 2015 , 297 : 80 - 94 ．

ZHU H G , ZHAO Y R , SONG Y J ． 2D logistic-modulated-sinecoupling-logistic chaotic map for image encryption ［J］． IEEE Access , 2019 , 7 : 14081 - 14098 ．

WANG C F , DING Q ． A class of quadratic polynomial chaotic maps and their fixed points analysis ［J］． Entropy (Basel,Switzerland) , 2019 , 21 ( 7 ): 658 ．

LI W S , YAN W H , ZHANG R X , et al ． A new 3D discrete hyperchaotic system and its application in secure transmission ［J］． International Journal of Bifurcation and Chaos , 2019 , 29 ( 14 ): 1950206 ．

LIU C Y , DING Q ． A color image encryption scheme based on a novel 3D chaotic mapping ［J］． Complexity,2020 , 2020 :3837209．

WANG C F , FAN C L , DING Q ． Constructing discrete chaotic systems with positive Lyapunov exponents ［J］． International Journal of Bifurcation and Chaos , 2018 , 28 ( 7 ): 1850084 ．

HUA Z Y , CHEN Y Y , BAO H , et al ． Two-dimensional parametric polynomial chaotic system ［J］． IEEE Transactions on Systems,Man,and Cybernetics:Systems , 2022 , 52 ( 7 ): 4402 - 4414 ．

WOLF A , SWIFT J B , SWINNEY H L , et al ． Determining Lyapunov exponents from a time series ［J］． Physica D:Nonlinear Phenomena , 1985 , 16 ( 3 ): 285 - 317 ．

孙克辉．混沌信息传输原理与技术［M］．北京 : 清华大学出版社 , 2015 ．

SUN K H ． Principle and technology of chaotic secure communication ［M］． Beijing : Tsinghua University Press , 2015 ．

LAKE D E , RICHMAN J S , GRIFFIN M P , et al ． Sample entropy analysis of neonatal heart rate variability ［J］． American Journal of Physiology Regulatory,Integrative and Comparative Physiology , 2002 , 283 ( 3 ): 789 - 797 ．

RAMDANI S , SEIGLE B , LAGARDE J , et al ． On the use of sample entropy to analyze human postural sway data ［J］． Medical Engineering＆ Physics , 2009 , 31 ( 8 ): 1023 - 1031 ．

LACASA L , GÓMEZ-GARDEÑES J , ． Correlation dimension of complex networks ［J］． Physical Review Letters , 2013 , 110 ( 16 ): 168703 ．

于娜 , 丁群 , 陈红．异结构系统混沌同步及其在信息传输中的应用［J］．通信学报 , 2007 , 28 ( 10 ): 73 - 78 ．

YU N , DING Q , CHEN H ． Synchronization of different structure chaotic systems and the application in secure communication ［J］． Journal on Communications , 2007 , 28 ( 10 ): 73 - 78 ．

朱勇 , 王佳楠 , 丁群．新型的CD-DCSK混沌键控信息传输系统［J］．通信学报 , 2012 , 33 ( 5 ): 169 - 176 ．

ZHU Y , WANG J N , DING Q ． New kind of CD-DCSK chaos shift keying secure communication system ［J］． Journal on Communications , 2012 , 33 ( 5 ): 169 - 176 ．

LI G Z , ZHANG B ． A novel weak signal detection method via chaotic synchronization using chua’s circuit ［J］． IEEE Transactions on Industrial Electronics , 2017 , 64 ( 3 ): 2255 - 2265 ．

ZHANG X X , XU J ． An extended synchronization method to identify slowly time-varying parameters in nonlinear systems ［J］． IEEE Transactions on Signal Processing , 2018 , 66 ( 2 ): 438 - 448 ．

YANG H , JIANG G P ． Reference-modulated DCSK:a novel chaoticcommunication scheme ［J］． IEEE Transactions on Circuits and Systems II:Express Briefs , 2013 , 60 ( 4 ): 232 - 236 ．

浏览量

195

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

基于量子混沌映射降低OFDM系统PAPR的算法研究

基于混沌冗余和阈值控制的联合算术码双向编译码快速算法