# A Novel Intermittent Jumping Coupled Map Lattice Based on Multiple Chaotic Maps
## 1 Introduction  
In 1985, [PERSON] [1; 2; 3; 4; 5] formally proposed the Coupled Map Lattice (CML) consisting of discrete time steps, discrete spatial positions, and continuous state variables, and then deeply investigated its chaotic behavior. The series of studies [1; 2; 3; 4; 5] reveal that the CML system can create spatiotemporal chaos by combining local nonlinear dynamics and spatial diffusion. On the other hand, [PERSON] [6] set forth that chaotic systems have remarkable cryptography properties, including simple structure, ergodicity, and high sensitivity to initial conditions and control parameters, and then constructed a chaos-based permutation-and-diffusion cipher architecture for encrypting images. These pioneering achievements have been continuous sources that inspire subsequent methods [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29] and have enriched the field of chaotic cryptography. [PERSON] and [PERSON] [7; 8] proposed a Non-adjacent Coupled Map Lattice (NCML) in which the spatial positions of coupled lattices are dynamically determined through a nonlinear Arnold cat map. Then, the spatiotemporal chaotic sequences were used to drive a bit-level group permutation phase. [PERSON] et al. [9] redesigned the NCML system by replacing a Logistic map with a piecewise-linear chaotic map, in the hope of boosting the turbulence of local reaction. To increase the spatial diffusion, reference [10] provided a hybrid-coupling mechanism that considers the adjacent and non-adjacent interactions simultaneously. Later, [PERSON] et al. [11] employed a 3D Arnold cat map to establish coupling relations between lattices, which enlarges the chaotic regime over a wide range of parameters. In [12], [PERSON] et al. developed a NCML-based S-box shuffling method, which strengthens the ability to resist linear password attacks. [PERSON] et al. [13] put forward a Dynamically Coupled Map Lattice (DCML), in which the coupling coefficient dynamically varies with the spatiotemporal indices. Then, [PERSON] et al. [14] combined the ideas behind NCML and DCML, and inventeda Non-adjacent Dynamically Coupled Map Lattice (NDCML). In [15], the spatiotemporal chaotic sequences generated by the NDCML system were used to govern a bidirectional image diffusion phase. Along this line of thought, [PERSON] et al. [16] constructed a tailor-made dynamical coupling architecture, and claimed that it can evenly spread diffusion energies over lattices. Reference [17] described a customized globally CML whose coupling term is a superposition of multiple chaotic maps. [PERSON] et al. introduced a fractional order Logistic map into the CML system, and investigated the spatiotemporal dynamics conditioned on non-adjacent coupling [18] or time delay [19], respectively. Inspired by [19], [PERSON] et al. [20] defined a dedicated delay function, and developed a new CML system with time delay. This CML system [20] serves as a pseudo-random number generator for encrypting RGB images in a channel-crossed manner [21]. [PERSON] et al. [22; 23] focused on a kind of cross CML whose diffusion mechanism proceeds along the temporal and spatial dimensions simultaneously. A dynamical coupling coefficient controlled by Tent map [22] or a pair of module operations [23] was introduced into the cross CML in order to enhance the chaotic behaviors. Reference [24] presented a mixed CML, which organizes three chaotic maps together guided by the spatial positions of lattices. In addition, some works [25; 26; 27; 28; 29] extended the original CML system to two dimensions, and realized the deployment in some real-world applications like image encryption or hiding. In summary, the ideas of the above works [7; 8; 9; 10; 11; 13; 14; 16; 17; 22; 23; 24] mainly concentrate on three aspects: non-adjacent coupling [7; 8; 9; 10; 11], dynamical coupling [13; 14; 16; 22; 23], and multi-chaos mixing [17; 24]. Based on our analysis, there still exist some problems in the three aspects.