Modeling,dynamic Analysis And Image Encryption Of Complex Chaotic System

The randomness of chaos makes it have a broad application prospect in many fields,especially in communication cryptography.According to the type and number of equilibrium points,autonomous chaotic systems can be divided into two types: selfexcited dissipative systems with self-excited attractors and hidden chaotic systems with hidden attractors.If there are two or more positive Lyapunov exponents in a chaotic system,the system will be transformed into a more complex hyperchaotic system.Compared with chaos system,hyperchaos system has more abundant dynamic behavior and wider application space,so the research of hyperchaos system is very meaningful and necessary.This paper mainly constructs several chaotic systems,including self-excited chaotic system and hidden chaotic system.The system is a common vortex attractor similar to the famous Lorenz shape.The detailed mechanism analysis and numerical simulation of its chaos are carried out,and the model is applied to video encryption.The specific content of this paper is as follows:(1)A four-dimensional self-excited hyperchaos model is constructed,and trigonometric function is introduced to construct a chaotic system with infinite number of equilibrium points.Lyapunov index,bifurcation diagram and Poincare interface are used to verify the chaotic characteristics of the system,and rich dynamic evolution is carried out.By using the principle of Li's index and the principle of optimization,the prediction bound of the transformed system is obtained,and the ellipsoid boundary of the system is calculated,and the existence of chaotic characteristics of the system is strictly proved by the topological horseshoe.(2)Several hidden chaotic systems are listed,which belong to the type of no equilibrium point or linear equilibrium point.The convergence,divergence and stability of the linear equilibrium point system are analyzed.The dynamic behavior of the system is verified by Lyapunov index and bifurcation diagram.The coexistence of attractors in the hidden chaotic system is found.The basin diagram is drawn according to the change of the initial value to show the influence of the initial value of the system.The trigonometric function is connected with the multi scroll,and the multi scroll extension in single or multiple directions is realized in the constructed hyperchaotic system.It is speculated that the system has the property of infinite scroll.(3)The application of video encryption to the hidden chaotic system is carried out.The key of the new hidden chaotic system is obtained through MATLAB simulation.The video plaintext information is scrambled and diffused to form ciphertext.The result display and security analysis of the encrypted ciphertext are carried out to verify that the new hidden chaotic system can be used in video encryption.