Zou Hailin, Gong Xiaofeng, Lai C-H
Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117543, Singapore.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Oct;82(4 Pt 2):046209. doi: 10.1103/PhysRevE.82.046209. Epub 2010 Oct 11.
Unstable attractors whose nearby points will almost leave the neighborhood have been observed in pulse-coupled oscillators. In this model, an oscillator fires and sends out a pulse when reaching the threshold. In terms of these firing events, we find that the unstable attractors have a simple property hidden in the event sequences. They coexist with active simultaneous firing events. That is, at least two oscillators reach the threshold simultaneously, which is not directly caused by the receiving pulses. We show that the split of the active simultaneous firing events by general perturbations can make the nearby points leave the unstable attractors. Furthermore, this structure can be applied to study the bifurcation of unstable attractors. Unstable attractors can bifurcate due to the failure of establishing active simultaneous firing events.
在脉冲耦合振荡器中观察到了附近点几乎会离开邻域的不稳定吸引子。在该模型中，一个振荡器达到阈值时会触发并发出一个脉冲。就这些触发事件而言，我们发现不稳定吸引子在事件序列中隐藏着一个简单特性。它们与活跃的同步触发事件共存。也就是说，至少有两个振荡器同时达到阈值，这并非由接收脉冲直接导致。我们表明，一般扰动对活跃同步触发事件的分裂会使附近点离开不稳定吸引子。此外，这种结构可用于研究不稳定吸引子的分岔。由于未能建立活跃的同步触发事件，不稳定吸引子会发生分岔。
