Hidden attractors in chaotic dynamical systems can be found by exploring the basin of attraction which has no intersect with any equilibria. Controlling chaos in these systems are complicated, which needs developed methods. In this paper, a 3D jerk system with only one stable equilibrium and hidden attractor is analyzed in infinity by the help of the Poincare compactification in R³. Meanwhile, a distributed delayed feedback (DDF) control scheme for this system is proposed. By using the center manifold theory of functional differential equation (FDE), Hopf bifurcation for the DDF control system is analyzed and obtained. Results confirm the accuracy of the bifurcation analysis and the effectiveness of the proposed DDF control strategy.

中文翻译：

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具有一个稳定平衡的混沌系统的无穷大动力学和DDF控制

通过探索不与任何平衡相交的吸引盆地，可以发现混沌动力学系统中的隐藏吸引子。这些系统中的混乱控制非常复杂，需要开发方法。在本文中，借助R ³中的Poincare压实，在无限远的情况下分析了只有一个稳定平衡和隐藏吸引子的3D冲击系统。同时，提出了该系统的分布式延迟反馈（DDF）控制方案。利用泛函微分方程（FDE）的中心流形理论，对DDF控制系统的Hopf分岔进行了分析和获得。结果证实了分叉分析的准确性以及所提出的DDF控制策略的有效性。