Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System

A multi-scroll attractor reflects the structural diversity of dynamic system, and multi-stability behavior its state diversity. Multi-scroll chaotic systems can produce complex random sequences, which have important application values in field data security. However, current works on multi-scroll–multi-steady been carried out separately, rather than simultaneously. This paper considers a three-dimensional Jerk system with sinusoidal nonlinear term. The basic behaviors, such as stability equilibrium points, bifurcation parameters initial values, phase diagrams, basins attraction, were analyzed. It was found that has infinite points. Moreover, not only generates dynamics, single-scroll, double-scroll, but also realizes self-reproduction these characteristics by controlling value system. Therefore, expanding point, effective controls system’s are realized at same time, having theoretical significance value.