Constructing n-dimensional discrete non-degenerate hyperchaotic maps using QR decomposition

Abstract

Lyapunov exponents (LEs) characterize the average exponential rate of convergence or divergence between adjacent orbits in phase space. Thus, the number of positive LEs can reflect the complexity of chaotic systems from a certain point of view. To resist the dynamic degradation of digital chaos, we propose a novel universal method that is based on QR decomposition for constructing non-degenerate hyperchaotic maps. A large number of positive LEs can be generated to increase the complexity of chaotic systems. Furthermore, we construct a 4-D discrete non-degenerate hyperchaotic map as an example to demonstrate the adaptability and efficacy of the proposed scheme. For the proposed method, the related control parameters can not only effectively adjust Lyapunov exponents, but also carry out chaotic regulation on the discrete map, such as amplitude control and offset boosting. In addition, a pseudorandom number generator (PRNG) is designed with desirable statistical properties. Then, a microcontroller-based platform was developed to implement the proposed chaotic map. This study is interesting and has a potential for real-world applications, such as secure communication and cryptography.