广义二维多项式混沌映射及其在信息传输中的应用

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

Abstract

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.

Key words: Lyapunov exponent, dynamic degradation, chaotic map, secure communication

CLC Number:

TN918

Wenhao YAN, Zijing JIANG, Xin HUANG, Shujuan ZHU, Qun DING. Generalized 2D polynomial chaotic map and its application in information transmission[J]. Journal on Communications, 2022, 43(9): 80-89.

Figures/Tables 12

References 30

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映射	初始值(x₀,y₀)	参数(a,b)	CD
Hénon映射	(0.4,0.3)	(1.4,0.3)	1.359 9
2D-SLM	(0.4,0.3)	(1,3)	1.546 2
LSMCL	(0.4,0.3)	(0.75 3)	1.491 4
本文映射	(0.4,0.3)	(49,49)	1.990 8

测试序号	测试项目	P值		结果
测试序号	测试项目	x序列	y序列	结果
1	频率	0.554 320	0.326 810	通过
2	组内频数	0.834 570	0.577 802	通过
3	游程	0.547 600	0.197 506	通过
4	组内最长游程	0.801 265	0.792 351	通过
5	二元矩阵秩	0.972 745	0.267 811	通过
6	离散傅里叶变换	0.035 687	0.948 721	通过
7	非重叠模板匹配	0.235 874	0.478 512	通过
8	重叠模板匹配	0.497 832	0.089 451	通过
9	通用统计	0.935 647	0.058 974	通过
10	线性复杂度	0.798 145	0.278 945	通过
11	串行	0.754 612	0.845 971	通过
12	近似熵	0.616 784	0.089 451	通过
13	累积和	0.168 745	0.944 513	通过
14	随机偏离	0.654 123	0.087 945	通过
15	随机偏离变量	0.565 209	0.058 799	通过

Generalized 2D polynomial chaotic map and its application in information transmission

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