Chaos, as an important subject of nonlinear science, plays an important role in solving problems in both natural sciences and social sciences such as the fields of secure communications, fluid motion, particle motion and so on. Aiming at this problem, this paper proposes a nonlinear dynamic system composed of product trigonometric functions and studies its chaotic characteristics. Through the mathematical derivation of the system’s period, the analysis of the necessary conditions at the fixed point, the experimental drawing of the Lyapunov exponential graph and the branch graph of the system, it is proved that the system has larger chaotic interval and stronger chaotic characteristics. The parameters of the proposed dynamic system are generated randomly, and then the chaotic sequence can be generated. The chaotic sequence is used to encrypt the digital image, a good encryption effect is obtained, and there is a large key space. At the same time, the motion of the particles in the space magnetic field is simulated, which further proves that the trigonometric system has strong chaotic characteristics.

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In order to improve the complexity of chaotic mapping and the security of image encryption algorithms, this paper proposes a new coupled three-dimensional chaotic system based on sine mapping and lorenz mapping. Based on this chaotic system, a new color image encryption algorithm is proposed, which performs index position scrambling and Arnold scrambling on the bit plane of the plaintext image, and then performs an XOR diffusion operation on the scrambled ciphertext to obtain the final ciphertext image. Simulation experiments show that the algorithm has a large key space, a small image correlation coefficient, an information entropy value of 7.9921, and a good encryption effect.

In this paper, we propose an image feature extraction method based on 3D chaotic attractor, and carry out face video recognition. By adjusting the auxiliary function, the feature point set is located on a plane in the 3D coordinate system. The experiment shows that the feature point set on the plane can extract face features better and recognize faces more efficiently. This method is faster and has higher recognition rate than the method that uses trigonometric function to iteratively generate image feature point set to recognize face in video.