###### Abstract  
This paper proposes a novel spatiotemporal chaotic system with two-dimensional dynamic pseudo-random coupled map lattices (2D-DPRCML) based on partitioned elementary cellular automata (PECA). In the system iteration, coupling lattices are chosen based on the chaotic PECA, and the iterative results of PECA are also employed as the perturbation for the system. We investigate the system's chaotic properties, including bifurcation diagrams, Kolmogorov-Sinai entropy density and universality. In addition, the output sequences were analyzed for uniformity and randomness. The correlations between the system lattices are also explored. The simulation results and theoretical analysis demonstrate that the 2D-DPRCML system possesses excellent chaotic performance, and the output sequences show good uniformity and randomness, indicating that the 2D-DPRCML system is capable of resisting the return maps attack. It is evident from all these advantages that the proposed system is ideal for use in cryptography. partitioned elementary cellular automata; two-dimensional coupled map lattices; dynamic pseudo-random coupling; spatiotemporal chaos +
Footnote †: journal: Applied Sciences  
In the spatiotemporal chaotic system, the mutual perturbation between different lattices enables the system to have a more complex dynamical behavior, which effectively alleviates the dynamical degradation. Since [PERSON] initially proposed the coupled map lattices (CMLs) in 1985 [25], an increasing number of scholars have studied them and designed CML-based spatiotemporal chaotic systems. In general, SC systems can be classified into two categories according to their dimensionality: one-dimensional (1D) [4; 26; 27] and high-dimensional [7; 28; 29]. In one-dimensional SC systems, the lattices have only one direction, so their processing capacity is limited. In high-dimensional SC systems, two-dimensional (2D) SC systems are the most common. They not only possess a larger lattice space, but also possess better chaotic properties which are more suitable for image encryption [30]. Compared to 1D CML, 2D CML possesses faster energy transfer rates. At the same time, the increased dimensionality can enhance the system's complexity and make it more difficult to be cracked by inverse operations. [PERSON]. [29; 30] developed a 2D nonlinear coupling scheme. In their scheme, the coupled approach is on the basis of the chaotic Arnold cat map, and this coupling approach reinforces the chaotic behavior of the system. However, although coupling is performed using the nonlinear function, the choice of the coupling lattices in each iteration is fixed because the parameters of the nonlinear function are fixed and iterate only once. Moreover, the periodic window is still present in its bifurcation diagram. Ref. [7] designed 2D mixed pseudo-random coupled map lattices based on the piecewise linear chaotic maps and Sin (PWLCM-Sin) map, which possesses excellent aperiodicity. In this coupling scheme, the choice of coupling lattice changes continuously with iteration, which significantly enhances the performance of the chaotic system. However, in the performance analysis of this system, its return map is easily recognizable, and the uniformity of its output sequences is not very good, indicating that it is sensitive to attacks based on the return map technique or statistics. Although the above schemes effectively alleviate dynamic degradation, with the development of computer technology, chaotic systems are increasingly vulnerable to attacks by phase space reconstruction or return map methods. [PERSON] et al. [31] utilized a conceptual network based on phase space reconstruction to forecast the time series produced by chaotic systems. In their scheme, the prediction accuracy is significantly improved. Moreover, [PERSON] et al. [32] proposed a modified return maps technique for estimating the parameters of chaotic systems. The modified approach can even estimate the parameters in the fractional-order chaotic system effectively.