Dynamic behavior of small system under the influence of parameters and application of image encryption

This paper presents a method for constructing chaotic systems under parameter conditions to investigate their impact on the dynamic behavior of small systems. The method allows for clear differentiation of small systems based on their parameter conditions. After selecting an appropriate system model, the dynamic behavior of the small system is described using equilibrium points, information entropy, Kolmogorov entropy, and complexity. The results demonstrate how the dynamic behavior of the small system changes under different initial conditions. To validate the universality of the construction method, the classical Lorenz system and Liu system are also applied, yielding satisfactory results. Furthermore, the paper applies the small system in a specific state to a plaintext correlation scrambling algorithm, exploring the simulation results and security performance of the chaotic image encryption system. The findings demonstrate the effectiveness of the small system in image encryption. This research provides a practical foundation for the construction method and application of small systems under specific parameter conditions.