This paper reports the complex dynamics of a class of two-dimensional maps containing hidden attractors via linear augmentation. Firstly, the method of linear augmentation for continuous dynamical systems is generalized to discrete dynamical systems. Then three cases of a class of two-dimensional maps that exhibit hidden dynamics, the maps with no fixed point and the maps with one stable fixed point, are studied. Our numerical simulations show the effectiveness of the linear augmentation method. As the coupling strength of the controller increases or decreases, hidden attractor can be annihilated or altered to be self-excited, and multistability of the map can be controlled to being bistable or monostable.

中文翻译：

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通过线性增强控制一类二维地图的隐藏动力学和多稳定性

本文通过线性增强报告了一类包含隐藏吸引子的二维地图的复杂动力学。首先，将连续动力系统的线性增广方法推广到离散动力系统。然后研究了一类具有隐动态特性的二维地图，即无不动点的地图和有一个稳定不动点的地图的三种情况。我们的数值模拟显示了线性增强方法的有效性。随着控制器耦合强度的增加或减少，隐藏的吸引子可以被消灭或改变为自激，并且可以将映射的多稳态控制为双稳态或单稳态。