A new memristor-based hyperchaotic system is described in this paper. After studying on its basic dynamic characteristics, it is found that the hidden attractors can be obtained by adding a nonzero parameter (which named optimized factor in this paper) to the system. Moreover, when the optimized factor is varying, the corresponding hidden attractors of the system is symmetrical and can convert between double scrolls and a single scroll. Further, the optimized memristor-based hyperchaotic system is implemented by analog circuits. Corresponding experimental results are completely consistent with the theoretical analysis.

A novel hyperchaotic circuit is proposed by introducing a memristor feedback in a simple Lorenz-like chaotic system. Dynamic analysis shows that it has infinite equilibrium points and multistability. Additionally, the symmetrical coexistent attractors are investigated. Further, the hyperchaotic system is implemented by analogue circuits. Corresponding experimental results are completely consistent with the theoretical analysis.

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To further improve the complexity of the chaotic system and broaden the chaotic parameter range, a novel logarithmic chaotic system was constructed by adding a nonlinear term of logarithm. The dynamic characteristics of the chaotic system were analyzed by chaotic phase diagram, bifurcation diagram, Lyapunov exponent spectrum, Poincaré mapping and dynamical map, etc. The system was digitized by DSP simulation, and the corresponding experimental results are completely consistent with the theoretical analysis. Furthermore, the equivalent hardware circuit was designed and theoretical analysis was verified by its experimental results.

In this paper a novel encryption scheme based on memristive hyperchaotic system was proposed. Firstly, combined with SHA-512 hash function and plain image, key sequences can be generated by iterating the memristive hyperchaotic system. Then, permutation operation and diffusion operation are performed for each row and column of the plain image. Finally, a serious of simulation experiments are conducted to evaluate the proposed encryption scheme, showing that the proposed scheme has well performance. Further, NIST SP800-22 test results show that the randomness of the hyperchaotic pseudorandom sequence used by the algorithm is better than the general linear congruence pseudorandom sequence.