Chaotic systems with variable indexs for image encryption application

A new chaotic system is obtained by changing the number of unknown parameters. The dynamical behavior of the chaotic system is investigated by the exponential change of the single unknown parameter and the state variable in the nonlinear term of the system. The structure of the newly constructed chaotic system is explored. When the number of the same state variables in the nonlinear term of the chaotic system varies, the system’s dynamic behavior undergoes complex changes. Moreover, with the exponential change of a single-state variable in a three-dimensional system, the system maintains the chaotic attractor while the state of the attractor changes. On this basis, the Lyapunov exponent, bifurcation diagram, complexity, and 0–1 test are used to compare and analyze this phenomenon. Through circuit simulations, the chaotic characteristics of the system under different conditions are further verified; this provides a theoretical basis for the hardware implementation of the new system. Finally, the new chaotic system is applied to an image encryption system with the same encryption and decryption processes. The comparison shows improved encryption and decryption characteristics of image encryption systems.