The design and circuit implementation of flexible chaotic systems with desired properties have been of great interest due to their promising applications in various chaos-based information systems. In this paper, a simple three-dimensional autonomous chaotic system with only one quadratic nonlinearity and six linear terms is proposed. The system is asymmetric, which has two equilibria and can generate a single-scroll attractor. This system exhibits asymmetric bi-stability behaviors of chaotic attractors coexisting with periodic limit cycles and other chaotic attractors. By introducing control functions to coefficients of specific linear term or quadratic term, the system can be extended as an amplitude-controllable, equilibrium-shiftable chaotic system. Consequently, attractor rotation is implemented via polarity symmetry, and pseudo-multi-scroll attractors are further generated via nonautonomous approach. The theoretical analyses are confirmed by both the numerical simulations and circuit verifications.

具有期望特性的柔性混沌系统的设计和电路实现由于其在各种基于混沌的信息系统中的应用前景而倍受关注。本文提出了一个只有一个二次非线性和六个线性项的简单三维自治混沌系统。该系统是不对称的，具有两个平衡点，并且可以生成单卷吸引子。该系统表现出与周期极限环和其他混沌吸引子共存的混沌吸引子的不对称双稳定性能。通过将控制函数引入特定线性项或二次项的系数，可以将该系统扩展为一个振幅可控制的，平衡移位的混沌系统。因此，吸引子旋转是通过极性对称实现的，伪多滚动吸引子是通过非自治方法进一步生成的。理论分析已通过数值模拟和电路验证得到证实。