ABSTRACT
Synchronization in networks of coupled oscillators is a fascinating topic in physics, social and technology network research community. A collective synchronization phenomenology is characterized by a population of coupled oscillators and a network model describing the link and interaction between the individuals. These two ingredients give rise to various dynamic behaviors. In particular, the collective synchronization modeled by epidemic process is a variation of the oscillator network. The earliest discussion of the periodic oscillations of epidemic model focus on small-world networks (Kuperman & Abramson 2001). They found that when rewiring probability slowly increases, the number of infected individuals will gradually change from fluctuations at a fixed point to apparent periodic oscillations with the time series. By using a modified SIR model, which is frequently used in the early epidemic dynamics research, the epidemic threshold pc for case of mean degree k = 2 on small world networks has been investigated (Zanette 2001).The above works provide us a new perspective to measure the smallworld effect, from the dynamics of system, not limited to the topological analyzing method.
