###### Abstract
To sum up, there is no doubt that the improvement of these schemes has brought security threats to chaotic encryption. In order to remedy the drawbacks mentioned above, a novel two-dimensional dynamic pseudo-random CML (2D-DPRCML) system is developed, and a new perturbation scheme is applied to this system. The computation of the index of the coupled lattice in this system is dynamic and pseudo-random, and it is based on the output of chaotic partitioned elementary cellular automata (PECA). Furthermore, the output of PECA is also employed to calculate perturbations. The approach in this paper is an extension and improvement of our previous work [33]. The two-dimensional coupling scheme proposed in this paper attempts to select coupling lattices at different orientations and positions pseudo-randomly, and a new perturbation algorithm is devised. The PECA designed in the proposed system can increase the perturbation period further compared to the elementary cellular automata used in the previous system. Additionally, in the previous system, the perturbation value of each lattice must be calculated separately in each iteration. However, in the proposed system, only one perturbation is computed per iteration, and the variation in the perturbation for different lattices is achieved by adding different symbols, which reduces the computational effort and speeds up the operation of the proposed system in comparison to the previous method. The points of innovation in this paper are as follows:  
* A partitioned elementary cellular automata (PECA) is designed for the coupling scheme and perturbation algorithm. The elementary cellular automata (ECA) [34] is only one-dimensional, and its data volume is insufficient for a two-dimensional SC system. Therefore, in this article, a special PECA with two different chaos rulesis devised. This chaotic PECA can generate two-dimensional iterative results with pseudo-randomness. * A new PECA-based dynamic pseudo-random coupling scheme is devised. Instead of employing fixed lattices for coupling, the lattices selected for coupling by the 2D-DPRCML system are determined by the iterative outputs of PECA. The PECA is iterated when calculating each lattice, so the process of selecting the coupling lattice by the system becomes dynamic and pseudo-random. Moreover, the 2D-DPRCML system can be reproduced as long as the initial values and local transition rules of PECA are known, which means that this system is applicable to cryptography. * A novel PECA-based perturbation algorithm is proposed. The iterative results of PECA are used to add different perturbations to each lattice in the DPRCML system. Such an approach brings several advantages. Firstly, the period window in the bifurcation graph vanishes, indicating the better aperiodicity of the proposed system. Secondly, according to certain analysis [12], the dynamical degradation is further alleviated. On the one hand, PECA is essentially a discrete dynamical system whose iterations are not affected by the precision of digital systems, so there is no degradation in PECA. On the other hand, some special local transition rules of the ECA lead to chaos [34], which is pseudo-random and unpredictable. Thirdly, the correlation among different lattices is considerably reduced due to the addition of different perturbations to individual lattices. Fourthly, the fixed shape in the return map is broken. In addition, a remarkable enhancement of uniformity and randomness is achieved by this system. In conclusion, the PECA-based perturbation improves the unpredictability and complexity of the 2D-DPRCML system, which can effectively resist the attack of phase space reconstruction or the return maps method. The following contents of this paper are as follows: Section 2 presents the preliminary knowledge of 2D CML and PECA a complete description of the 2D-DPRCML system is presented in Section 3, Section 4 analyzes the performance of the 2D-DPRCML system and Section 5 summarizes the full article.