Heterogeneous and Homogeneous Attractors in 2D Sine-Based Hyperchaotic Map and Its High-Precision FPGA Implementation

This study introduces a two-dimensional sine-based hyperchaotic map (2D-SBHM), which leverages the boundedness and periodicity of sinusoidal functions to enhance chaotic performance. The 2D-SBHM exhibits multiple fixed points, with variations in system parameters (SPs) inducing diverse bifurcation behaviors. Numerical analysis reveals a maximal chaotic range of -40, 40 and a high permutation entropy of 6.433, outperforming several existing 2D sine-based maps in stochastic metrics. The coexistence of attractors, including heterogeneous and homogeneous types derived from SPs, is explored. Four cases of homogeneous attractors generated from initial states are presented. A modular arithmetic method is proposed for generating homogeneous attractors, allowing the creation of attractor sets in quantities such as 3, 5, 15, 20, or 30. Furthermore, a high-precision hardware implementation strategy using FPGA and DAC architectures is developed, enabling theoretical calculations for oscilloscope amplitude scaling and display area. An FPGA-based hardware platform is constructed to verify the proposed approach and realize a pseudo-random number generator with a throughput rate of 2.8 Gbps. To the best of our knowledge, this work represents the first demonstration of arbitrary homogeneous attractor generation in a discrete chaotic map using modular arithmetic, coupled with the first high-precision hardware implementation of chaotic attractors.