Biblio

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.

Deterministic chaotic systems have been studied and developed in various fields of research. Dynamical systems with chaotic dynamics have different applications in communication, security and computation. Chaotic behaviors can be created by even simple nonlinear systems which can be implemented on low-cost hardware platforms. This paper presents a high-speed and low-cost hardware of three-dimensional chaotic flows without equilibrium. The proposed chaotic hardware is able to reproduce the main mechanism and dynamical behavior of the 3D chaotic flows observed in simulation, then a Chaotic Pseudo Random Number Generator is designed based on a 3D chaotic system. The proposed hardware is implemented with low computational overhead on an FPGA board, as a proof of concept. This low-cost chaotic hardware can be utilized in embedded and lightweight systems for a variety of chaotic based digital systems such as digital communication systems, and cryptography systems based on chaos theory for Security and IoT applications.