Exploring the Critical Sensitivity in Small-World Networks

Catastrophic phenomena such as earthquakes, avalanches, and critical points in the stock market are hard to predict. Recently, Xia et al. Pure Appl. Geophys. 159(2002)2491 showed that a geometrical system near catastrophic rupture presents a general critical sensitivity: the system becomes significantly sensitive near the catastrophe transition. Here we report that the phenomenon of critical sensitivity also exists in small-world network systems. With the increase of the small-world rewiring probability p, from the regular network p=0 to the random one p=1, the system performs more sensitively before the critical point while remaining in better organization through the evolutional progress, and the prediction threshold P_s performs more in advance. The concept of critical sensitivity can be applied to other complex network systems.