不连续映象系统中稳定不规则瞬变的动力学形成
Dynamical formation of stable irregular transients in discontinuous map systems
摘要：
稳定混沌是指在某些高维动力系统中经常观察到的具有负最大李雅普诺夫指数的长的不规则瞬态。这种现象背后的机制迄今尚未得到很好的研究。本文研究耦合不连续映象系统中稳定不规则瞬变的动力学形成。有趣的是，它被发现，瞬态动力学在相空间中有一个隐藏的模式：它反复接近盆地边界，然后从相空间中的一个遥远的区域跳跃。通过测量轨迹和盆地边界之间的距离序列，可以清楚地看到这种模式。稳定混沌的动力学形成来源于不连续边界与其像的交点。我们进行了数值实验来验证这一机制。
英文摘要：
Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so far. In this paper, we investigate the dynamical formation of stable irregular transients in coupled discontinuous map systems. Interestingly, it is found that the transient dynamics has a hidden pattern in the phase space: it repeatedly approaches a basin boundary and then jumps from the bundary to a remote region in the phase space. This pattern can be clearly visualized by measuring the distance sequences between the trajectory and the basin boundary. The dynamical formation of stable chaos originates from the intersection points of the discontinuous boundaries and their images. We carry out numerical experiments to verify this mechanism.
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