Abstract
Based on the special structure of the variable-boostable chaotic system VB19, that includes a smooth secondary flux-controlled memristor, a three-dimensional memristive chaotic system with only one equilibrium point is constructed. Numerical analysis reveals that the system has novel dynamical characteristics of controlling multiple types of attractors by a single parameter. At the same time, the existence of multiple transient behaviors and the coexistence of periodic and quasi-periodic attractors significantly increase the complexity of the system. Moreover, the system has a large range of high complexity phenomena, which is relatively rare in low-dimensional chaotic systems. A circuit is designed and implemented for this system in the physical circuit. Finally, this memristive system is applied to image encryption, whose excellent performance is demonstrated by key space, key sensitivity analysis, histogram analysis, and correlation coefficient analysis, which provides a reference for the further research of low dimensional memristive systems in the field of image encryption.
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