Research on discrete memristor models applied to discrete maps deserves more in-depth discussion. In this paper, a continuous memristor is introduced and the discrete memristor model is obtained by the forward Eulerian difference algorithmic discretization. This model is coupled to a cosine map to further obtain a two-dimensional memristor cosine map. The dynamical characteristics of the memristor cosine map are investigated through numerical simulations and other analytical methods. For example, the phase diagram, the bifurcation diagram, the Lyapunov exponential spectrum and the Spectral Entropy complexity with parameters, etc., In addition, multi-stability phenomena of the system are identified. The results show that the cosine map coupled with a discrete memristor has more complex dynamical behaviors and is more suitable for applications in cryptography.

In this paper, a hyperchaotic circuit consisting of a series memristor, meminductor, and memcapacitor is proposed. The dimensionless mathematical model of the system is established by the state equation of the circuit. The stability of equilibrium point of the system is analyzed by using the traditional dynamic analysis method. Then, the dynamical characteristics of the chaotic system with parameters are analyzed in detail. In addition, the system also has some particular phenomena such as attractor coexistence and state transition. Finally, the circuit is realized by DSP, and the result is consistent with that of numerical simulation. This proves the accuracy of the theoretical analysis. Numerical simulation result shows which hyperchaotic system has very abundant dynamical characteristics.

To address the consumption and security of color images for transmission and storage, a cross-channel color image encryption scheme based on a discrete memristive coupled neuron model and DWT compression is designed in this article. Firstly, the dynamics of the discrete memristive coupled neuron system are analyzed and found to possess the hyperchaotic phenomenon, which provides sufficient security for the encryption scheme. Secondly, the color image processed by discrete wavelet transform (DWT) has a quarter of the previous capacity. Then, the color image is combined with a Hash function, and the resulting Hash sequence is given the initial value of the hyperchaotic system. Next, a particle swarm foraging algorithm (PSFA) is designed to better disrupt the correlation in the RGB channel. Finally, a complementary DNA coding rule is implemented for the further encryption of color images. Simulation results show that even with DWT lossy compression, the recovered image can be clearly seen. The performance analysis illustrates that under the hyperchaotic system, the proposed encryption algorithm brings higher security for color images.

In this paper, an efficient image compression encryption scheme is proposed. Firstly, compressing the image by using BP neural network before encryption, which not only saves the subsequent encryption and decryption time but also minimizes storage and transmission space. Secondly, Chialvo neuron model is used to generate chaotic sequences for the encryption process in the scheme, confusing the compressed image according to a confusion algorithm combining single-plane and cross-plane. Next, diffusing the confused image. Subsequently, the diffused image and chaotic sequences are DNA encoded, performing DNA same or operation (DNA mutual mutations) and DNA mutations (DNA self-mutations). Finally, the DNA mutations results are decoded to obtain the cipher image. Security tests and compression performance analysis show that the scheme can efficiently and securely compress and encrypt images of different sizes with higher reconstruction quality compared to other compression schemes.