Zou Hailin, Guan Shuguang, Lai C-H
Department of Physics, National University of Singapore, Singapore, Singapore.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046214. doi: 10.1103/PhysRevE.80.046214. Epub 2009 Oct 23.
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 boundary 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.
稳定混沌是指具有负的最大李雅普诺夫指数的长时不规则暂态，通常在某些高维动力系统中观察到。迄今为止，这一现象背后的机制尚未得到充分研究。在本文中，我们研究了耦合不连续映射系统中稳定不规则暂态的动力学形成。有趣的是，发现暂态动力学在相空间中具有一种隐藏模式：它反复接近一个吸引子边界，然后从该边界跳转到相空间中的一个遥远区域。通过测量轨迹与吸引子边界之间的距离序列，可以清楚地可视化这种模式。稳定混沌的动力学形成源于不连续边界及其像的交点。我们进行了数值实验来验证这一机制。
