Design of memristor hyperchaotic circuit with burst oscillation and infinite attractor coexistence and its application

Abstract

A 4D hyperchaotic system with symmetry based on memristors is proposed and the chaotic properties of the circuit are verified by phase diagrams, Poincaré cross sections, bifurcation, Lyapunov exponents, and 0–1 tests. In addition, the system is found to have rich dynamical behaviors such as transient chaos, intermittent chaos, offset enhancement, burst oscillation, and infinite attractor coexistence. The complexity comparison analysis reveals that this hyperchaotic system has good symmetry as well as the initial values of the system that are more suitable for image encryption. Circuit simulation of the system using simulation software proved the usability of the system. A field programmable gate array (FPGA) is used to implement the actual digital circuit of the system. The final FPGA results agree with the numerical simulation and prove the practical value of the constructed memristor hyperchaotic system. Finally, chaotic circuits are applied to DNA image encryption. It is discovered to have a very large key space, strong key sensitivity, outstanding anti-cropping, noise immunity and high security performance. Thus, the proposed hyperchaotic system has good advantages for application in the field of image encryption.