新型一维偏移耦合映像格系统及其动态特性

混沌系统具有复杂的动力学行为，但在数字系统中运行时会出现动力学特性退化的问题。元胞自动机在时间、空间上都具有离散性，能够有效减弱混沌系统在有限精度下的动力学退化问题。基于元胞自动机，提出了一种一维偏移耦合映像格系统，利用初等元胞自动机每次更新的不同状态，动态产生每个格子的耦合索引偏移量，再根据偏移量对混沌序列施加不同的扰动，然后交替切换元胞自动机的迭代规则。最后，对混沌系统的动力学特性进行对比分析以及对该系统产生的时间序列进行量化和随机性检测，仿真实验结果表明，该混沌系统周期更长，遍历性更好，产生的序列随机性更佳，在序列密码算法中有很大的应用价值。

Novel one-dimensional migration-coupled mapping lattice system and its dynamic characteristics

Chaos systems demonstrate complex dynamic behavior, but they undergo a degradation of dynamic characteristics when operating in digital systems. Cellular automata, with their discrete nature in both time and space, can effectively mitigate the issue of dynamic degradation in chaotic systems under finite precision. Based on cellular automata, this paper proposed a one-dimensional offset-coupled lattice system with a mapping function. This system dynamically generated coupling index offsets for each cell by utilizing the distinct states of the elementary cellular automaton during each iteration. Then, it applied different perturbations to the chaotic sequence based on these offsets and alternates the iteration rules of the cellular automaton. Finally, through comparative analysis of the dynamic characteristics of the chaotic system and quantification and randomness testing of the generated time series, the simulation results demonstrate that this chaotic system exhibits longer periods, improved traversal properties, and superior randomness in the generated sequences. It has significant application value in sequence encryption algorithms.