An Anti-Degradation Chaotic Map and Its Statistical Robustness Analysis

Limited computing resources and device performance constraints, along with the increasing demand for real-time applications, pose challenges for chaos-based applications affected by dynamical degradation in digital platform scenarios. To address this issue, we first introduce an indicator called “Rate of Ergodicity (RoE),” which measures the degradation of a digital chaotic system under conditions of finite computational precision. Through the application of logistic map and several recent representative examples, it is demonstrated that these systems are prone to dynamical degradation when the calculation precision is limited. Second, a new chaotic map is constructed, which is shown through theoretical and experimental evidence to possess not only superior chaotic properties but also anti-degradation properties without requiring any additional operations. Thirdly, this new chaotic map is applied to a pseudorandom number generator to validate its anti-degradation capabilities under low computational precision. Finally, the digital hardware platform digital signal processor (DSP) is utilized to verify its physical realizability.