n-dimensional hyperchaotic discrete map with desired positive Lyapunov exponents and application to UART secure communication

When applying chaotic sequences in engineering applications, it is commonly imperative for chaotic systems to possess continuous hyperchaotic intervals and adjustable dimensions. This study proposes a n-dimensional hyperchaotic discrete map (nD-HDM) utilizing triangular matrices and mode operations. The diagonal elements and mode values can effectively adjust Lyapunov exponents(LEs) and amplitude intervals of the nD-HDM. To illustrate the effectiveness of nD-HDM, two typical 4D-HDMs are examined by numerical computations. The findings indicate that both 4D-HDMs possess four positive LEs, continuous hyperchaotic intervals, controlled amplitude ranges, and controllable distribution characteristics. The generated state variables exhibit exceptional stochastic characteristics and successfully pass the TestU01 test. To further improve the attractor fractal structure of nD-HDM, strategies for controlling state matrix-based heterogeneous attractors and graph transformation-based homogeneous attractors are given. The offset boosting, amplitude, and rotational control of the attractor can also be achieved. Finally, we validate 4D-HDMs on an ARM-based hardware platform and design a pseudorandom number-based universal asynchronous receiver/transmitter(UART) physical layer secure communication.