A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

被引：7

作者：

Fan, Chunlei ^{[1
]}

Ding, Qun ^{[1
]}

机构：

[1] Heilongjiang Univ, Elect Engn Coll, Harbin 150080, Peoples R China

来源：

CHINESE PHYSICS B | 2023年 / 32卷 / 01期

基金：

中国国家自然科学基金;

关键词：

digital chaos; dynamic degradation; state-mapping graph; periodicity analysis; DEGRADATION; PERIODICITY; GENERATOR;

D O I：

10.1088/1674-1056/ac785c

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Chaotic maps are widely used to design pseudo-random sequence generators, chaotic ciphers, and secure communication systems. Nevertheless, the dynamic characteristics of digital chaos in finite-precision domain must be degraded in varying degrees due to the limited calculation accuracy of hardware equipment. To assess the dynamic properties of digital chaos, we design a periodic cycle location algorithm (PCLA) from a new perspective to analyze the dynamic degradation of digital chaos. The PCLA can divide the state-mapping graph of digital chaos into several connected subgraphs for the purpose of locating all fixed points and periodic limit cycles contained in a digital chaotic map. To test the versatility and availability of our proposed algorithm, the periodic distribution and security of 1-D logistic maps and 2-D Baker maps are analyzed in detail. Moreover, this algorithm is helpful to the design of anti-degradation algorithms for digital chaotic dynamics. These related studies can promote the application of chaos in engineering practice.

引用

页数：10

共 30 条

[1] A novel high speed Artificial Neural Network-based chaotic True Random Number Generator on Field Programmable Gate Array [J].

Alcin, Murat ;

Koyuncu, Ismail ;

Tuna, Murat ;

Varan, Metin ;

Pehlivan, Ihsan .

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, 2019, 47 (03) :365-378

[2] Gb/s One-Time-Pad Data Encryption With Synchronized Chaos-Based True Random Bit Generators [J].

Argyris, Apostolos ;

Pikasis, Evangelos ;

Syvridis, Dimitris .

JOURNAL OF LIGHTWAVE TECHNOLOGY, 2016, 34 (22) :5325-5331

[3] Permutation entropy: A natural complexity measure for time series [J].

Bandt, C ;

Pompe, B .

PHYSICAL REVIEW LETTERS, 2002, 88 (17) :4

[4] Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting [J].

Bayani, Atiyeh ;

Rajagopal, Karthikeyan ;

Khalaf, Abdul Jalil M. ;

Jafari, Sajad ;

Leutcho, G. D. ;

Kengne, J. .

PHYSICS LETTERS A, 2019, 383 (13) :1450-1456

[5] Design and Smartphone Implementation of Chaotic Duplex H.264-Codec Video Communications [J].

Chen, Baoju ;

Yu, Simin ;

Zhang, Zeqing ;

Li, David Day-Uei ;

Lii, Jinhu .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (03)

[6] Analyzing the period distribution of digital chaos with graph theory [J].

Fan, C. L. ;

Ding, Q. .

PHYSICA SCRIPTA, 2021, 96 (08)

[7] Evaluating the Randomness of Chaotic Binary Sequences Via a Novel Period Detection Algorithm [J].

Fan, Chunlei ;

Ding, Qun ;

Tse, Chi K. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2022, 32 (05)

[8] Analysis and resistance of dynamic degradation of digital chaos via functional graphs [J].

Fan, Chunlei ;

Ding, Qun .

NONLINEAR DYNAMICS, 2021, 103 (01) :1081-1097

[9] Small world of Ulam networks for chaotic Hamiltonian dynamics [J].

Frahm, Klaus M. ;

Shepelyansky, Dima L. .

PHYSICAL REVIEW E, 2018, 98 (03)

[10] ROUNDOFF-INDUCED PERIODICITY AND THE CORRELATION DIMENSION OF CHAOTIC ATTRACTORS [J].

GREBOGI, C ;

OTT, E ;

YORKE, JA .

PHYSICAL REVIEW A, 1988, 38 (07) :3688-3692

← 1 2 3 →