| Title | Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Li, Chengqing, Feng, Bingbing, Li, Shujun, Kurths, Jüergen, Chen, Guanrong |
| Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |
| Volume | 66 |
| Pagination | 2322—2335 |
| ISSN | 1558-0806 |
| Keywords | black box, black box encryption, chaos, chaotic communication, chaotic dynamics, chaotic map, communication securiy, complex network, composability, cryptography, Degradation, digital computer, discrete-time chaotic maps, dynamics degradation, Encryption, fixed point arithmetic, fixed-point arithmetic, floating point arithmetic, floating-point arithmetic, Generators, logistic map, Logistics, Metrics, Orbits, pseudo-random number generator (PRNG), pseudorandom number generators, pubcrawl, Quantization (signal), random number generation, randomness, resilience, Resiliency, SMN, state-mapping network, telecommunication security, tent map |
| Abstract | Chaotic dynamics is widely used to design pseudo-random number generators and for other applications, such as secure communications and encryption. This paper aims to study the dynamics of the discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, also helping to classify and improve the randomness of pseudo-random number sequences generated by iterating the chaotic maps. |
| DOI | 10.1109/TCSI.2018.2888688 |
| Citation Key | li_dynamic_2019 |
Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks