A new hyperchaotic circuit with two memristors and its application in image encryption

Memristor is a kind of resistance with a memory function and its special properties decide its broad prospect for application. At present, the focus and difficulty of the research in memristor lie in the establishment of new models and related applications. Therefore, in this paper a new continuous and smooth memristor model is put forward first and the correctness of this new model is proved through the study in the phase trajectory relationship between voltage and current. Then based on Chua’s circuit, a new fifth-order hyper-chaotic circuit including two new memristor models is designed and the dimensionless mathematical model is deduced. By the classical nonlinear method of circuit analysis, the dissipation of the new system is put into study in this paper. It is proved through numerical simulation, bifurcation diagram, Lyapunov spectrum that the new system has its unique dynamical behavior. At last, chaotic sequence of the new system is used to encrypt the image and the encrypted histogram, the correlation and anti-attack capability between adjacent pixels and the key sensitivity are emphatically analyzed. It turns out that when applied to image encryption, the newly proposed memristor chaotic system has relatively high safety performance.