Abstract: On the basis of a generalized third-order Rucklidge system, a fourth-order hyperchaotic circuit system based on an quadratic nonlinear active magnetron memristor is proposed. The dynamics characteristics of the system, such as system phase diagram, Lyapunov exponential spectrum, bifurcation diagram, and coexisting attractor are studied by numerical simulation. The analysis results show that the system has rich dynamics characteristics and new topological structure. The system's circuit is designed and implemented by using Multisim circuit simulation software and FPGA digital hardware circuit. The experimental consequences are very consistent with the numerical simulation results. Finally, an image encryption algorithm is designed by combining scrambling-diffusion algorithm with DNA encryption. The new system chaotic sequence is used to encrypt image, and the encryption histogram, correlation between adjacent pixels, sensitivity, robustness and information entropy are analyzed. The results show that the new system is very sensitive to both chaotic key and plaintext, and the key space is large. The proposed chaotic system has high security performance when applied to image encryption.

Key words: hyperchaotic system, dynamic behavior, circuit implementation, image encryption, DNA dynamic coding