Self-excited and hidden multi-scroll attractors in a novel extremely simple three-dimensional system

Abstract

Multi-scroll hidden attractor (MSHA) system generally exhibits unpredictable motion trajectories and complex dynamical characteristics, which holds promising application prospects in information encryption. However, there are still some issues, such as complex structure and difficulty in regulation. Thus, constructing simple MSHA systems with complex dynamics has become a research focus in recent years. In this article, a new simple multi-scroll chaotic system with only one sinusoidal non-linear term is proposed. In particular, with respect to different system parameters, the proposed system can generate self-excited or hidden multi-scroll attractors flexibly. Furthermore, periodic or chaotic states can be observed within individual scrolls of multi-scroll attractor, depending on the various system parameters. In addition, both the system parameters and the transient simulation time can be conveniently adjusted to control the scroll counts. It should be noted that the proposed simple three-dimensional chaotic system can exhibit interesting initial-boosted dynamic behavior. Also, the coordinates of the attractor can be shifted due to offset-boosted behavior. This can be achieved by adjusting the independent non-bifurcated parameter $d$. Both initial-boosted and offset-boosted behaviors are capable of altering the location of the attractor within the state space without transforming its shape. This implies that the scope of state variable values can be easily adjusted, potentially offering significant convenience to engineering applications. Finally, an analog circuit has been designed to realize the suggested multi-scroll chaotic system. The results further attest to the operability of the system on the physical platform and the reliability of numerical analysis.