Physical images of relative timescales in coevolution dynamics

In this paper, we propose three physical images, namely, asymmetric external inputs, discretization of the low rate region, and secondary outbreak, to understand the mystery of the relative timescales in the coevolution dynamics on multiplex networks. We carry out our analysis on an irreversible information-epidemic coevolution dynamics. In this dynamics, we found five kinds of anomalous behaviors, which are that with the increase of relative information processing speed, the final epidemic size may be monotonically increasing, monotonically decreasing, first decreasing and then increasing, first increasing and then decreasing but increasing again, and suddenly increasing with large fluctuation. Such complex behavior can be fully explained by our three physical images. Moreover, these five behaviors may transform into one another, which is far more complex than cyclic dynamics. Of course, our physical images easily provide an explanation for the results of cyclic coevolution dynamics. Since our discussion does not rely on specific dynamics and networks, our research may readily be extended to a broader field, rather than the network epidemiology in this paper.