## 1 Introduction  
With the rapid development of information technology, digital images have become increasingly important in modern communication as an intuitive and efficient means of information transmission [1]. Consequently, the demand for secure transmission of digital images is also increasing. To ensure the security and confidentiality of images, technologies such as data hiding, digital watermarking, and image encryption have emerged [2]. Among these, image encryption is a crucial algorithm for protecting image information security. Since color images contain a wider range of information and are more prevalent than grayscale images, the encryption of color images has become a hot research area [3, 4]. The complex dynamical behavior exhibited by chaotic systems includes sensitivity to initial conditions, pseudo-randomness, and ergodicity. These features make chaotic systems important in various fields, such as cryptography, data compression, and image processing [5; 6; 7]. Systems with larger chaotic ranges are less susceptible to external attacks, and the chaotic properties are more stable, which can be used to encrypt images [8]. As a nonlinear component, the memristor has attracted much attention since its introduction due to its potential to construct chaotic systems with more complex and diverse dynamics [9; 10]. In this context, a large number of studies on chaotic systems based on memristors have emerged [11; 12; 13]. However, due to the insufficient complexity of the chaotic behavior in most systems, its application in image encryption is not very satisfactory [14; 15; 16; 17]. Therefore, a 2D hyperchaotic model with complex dynamical behavior based on a memristor model is proposed in this paper. In addition to chaotic systems, encryption algorithms are also particularly important. Previous studies have shown that many image encryption algorithms based on chaotic systems have some limitations, such as incomplete chaos, insufficient key space and so on. [PERSON] et al. proposes a multi-image encryption algorithm based on a novel fractional-order three-dimensional Lorenz chaotic system and a two-dimensional discrete polynomial hyperchaotic map [18]. However, the instability in the UACI and NPCR values indicates that the encryption algorithm's sensitivity to input changes is insufficient. As a result, the security of the algorithm is unstable and may be vulnerable to potential attacks. [PERSON] et al. presented a novel Rubik's Cube-like permutation method based on a novel cryptosystem (3 DVSCS-IES) [19]. However, its scrambling is not thorough enough, leading to its weak resistance to cropping. [PERSON] et al. presented a new color image encryption method by combining 2D chaotic map and compressed sensing [20]. Nevertheless, the inadequate key space used in encryption leads to its susceptibility to statistical attacks. [PERSON] et al. constructs a new two-dimensional chaotic map based on the interleaving of cosine and sine functions, utilizing two independent trigonometric functions without the need for composite operations [21]. While the chaotic map has a simple structure, its relatively low Lyapunov exponents suggest weak chaotic dynamics, which could impact its effectiveness in applications like secure communication. Based on the above problems, this paper proposes the SEME-TDHM algorithm that combines single-channel stochastic processing with multi-channel stochastic processing based on chaotic systems with complex dynamical behavior. The subsequent section outlines the contributions and innovations of this paper:  
1. This paper presents a 2D hyperchaotic map integrated with a memristor model. The map exhibits complex chaotic behavior and offers a wide range of parameter choices. A framework based on this map is proposed, enabling the exploration of additional chaotic maps with superior performance and laying the groundwork for further studies on similar systems. 2.