This paper presents a novel three-dimensional hyperchaotic map with the spherical attractor. The typical dynamic properties of the new chaotic system are evaluated by attractor diagrams, Lyapunov exponent (LE), bifurcations and permutation entropy (PE) complexity. The results show that it has rich dynamical behaviors, including hyperchaos, large Lyapunov exponent and typical bifurcations. There are also some unusual features, such as coexisting attractors and plane equilibrium. To improve its performance, we extend the attractor space by adding the staircase wave function to the new system. Compared with the original system, the expanded system has a larger complexity and more complex topology. By controlling the system parameters, it can effectively improve the PE complexity of the system. Finally, the digital circuit of the new system is realized based on DSP technology, and the feasibility of the system model is verified. The proposed hyperchaotic map has advantages in comple...

中文翻译：

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具有球形吸引子的超混沌映射的动力学

本文提出了一种新颖的带有球形吸引子的三维超混沌映射。通过吸引子图，李雅普诺夫指数（LE），分叉和置换熵（PE）复杂性来评估新混沌系统的典型动力学特性。结果表明，它具有丰富的动力学行为，包括超混沌，大的Lyapunov指数和典型的分叉。还有一些不寻常的特征，例如共存吸引子和平面平衡。为了提高其性能，我们通过在新系统中添加阶梯波函数来扩展吸引子空间。与原始系统相比，扩展后的系统具有更大的复杂性和更复杂的拓扑。通过控制系统参数，可以有效地提高系统的PE复杂度。最后，基于DSP技术实现了新系统的数字电路，并验证了系统模型的可行性。提出的超混沌映射在完成...方面具有优势。