基于分区初等元胞自动机的二维伪随机耦合映像格系统及其动态特性

Two-dimensional pseudo-random coupled map lattices system based on partitioned elementary cellular automata and its dynamic properties

针对基于耦合映像格的时空混沌系统中,某些控制参数会导致弱混沌的现象,以及系统生成序列频率分布不均的情况,提出了一种基于分区初等元胞自动机的二维伪随机耦合映像格系统。首先,基于初等元胞自动机,设计了高维的分区初等元胞自动机。然后,根据该高维自动机的输出,实现了伪随机的耦合方案,同时将自动机的输出作为扰动添加至时空混沌系统中。利用K熵、分岔图等对二维伪随机耦合映像格系统的动态特性进行了对比分析,同时对系统生成序列的分布特性、相关性以及随机性进行了研究。结果表明,该系统建立了更强更广泛的混沌特性,拥有良好的复杂性、遍历性和非周期性。此外,该系统生成的序列具有更均匀的分布和序列之间更低的相关性,并拥有良好的伪随机性。因此,二维伪随机耦合映像格系统在密码系统和混沌保密通信中具有广阔的应用前景。

To solve the weak chaos in the spatiotemporal chaotic system based on coupled map lattices under some control parameters and the un-uniformity of sequences generated by the coupled map lattices,a two-dimensional pseudo-random coupled map lattices(2D-PRCML)system was proposed.Firstly,the two-dimensional partitioned elementary cellular automata(2D-PECA)was designed to establish pseudo-random coupling.Secondly,iterative results of 2D-PECA were utilized to perturb the 2D-PRCML system.The chaotic behaviors of the proposed system,such as the bifurcation diagram,Kolmogorov-Sinai entropy,were investigated.Moreover,the uniformity of sequences generated by the 2D-PRCML system was discussed,and the correlation coefficients between any two sequences generated by different lattices were acquired.The analyses and tests indicate that the 2D-PRCML system exhibits stronger chaotic behavior.Furthermore,the sequence generated by the proposed system possesses better uniformity,randomness,and unpredictability.The outstanding properties of the 2D-PRCML system prove that it is more suitable for applying in cryptography and chaotic secure communication.