An internal perturbation method to counteract the dynamical degradation of digital chaotic maps and its application

To address the issue of dynamical degradation in digital chaotic maps, we propose a novel internal perturbation method. In this method, the system states and iteration times are utilized to perturb the parameters of the chaotic maps, which can effectively increase their complexity and period length. Some low-dimensional and high-dimensional chaotic maps are chosen as examples to verify the effectiveness of this method, and their dynamics are analyzed. The simulation results indicate that these improved chaotic maps exhibit a larger chaotic range and complexity compared to their original chaotic maps, and have longer period lengths and smaller auto-correlation than their digital chaotic maps at 8-bit precision. To further verify its feasibility and application value, the improved chaotic maps are implemented on field-programmable gate array, and applied to pseudo-random number generator at finite precision.