A Wide-Range Adjustable Conservative Memristive Hyperchaotic System with Transient Quasi-Periodic Characteristics and Encryption Application

In comparison with dissipative chaos, conservative chaos is better equipped to handle the risks associated with the reconstruction of phase space due to the absence of attractors. This paper proposes a novel five-dimensional (5D) conservative memristive hyperchaotic system (CMHS), by incorporating memristors into a four-dimensional (4D) conservative chaotic system (CCS). We conducted a comprehensive analysis, using Lyapunov exponent diagrams, bifurcation diagrams, phase portraits, equilibrium points, and spectral entropy maps to thoroughly verify the system's chaotic and conservative properties. The system exhibited characteristics such as hyperchaos and multi-stability over an ultra-wide range of parameters and initial values, accompanied by transient quasi-periodic phenomena. Subsequently, the pseudorandom sequences generated by the new system were tested and demonstrated excellent performance, passing all the tests set by the National Institute of Standards and Technology (NIST). In the final stage of the research, an image-encryption application based on the 5D CMHS was proposed. Through security analysis, the feasibility and security of the image-encryption algorithm were confirmed.