Epidemic spreading processes on multiplex networks have richer dynamical properties than those on single layered networks. To describe the intertwined processes on such networks, heterogeneous mean field (HMF) approach for continuous-time processes and microscopic Markov chain approach for discrete-time processes have been proposed. However, it has been shown that the time evolution of infected individuals and the final epidemic size obtained from these approaches have noticeable discrepancy comparing to those from Monte Carlo simulations. In this paper, we extend the approach of effective degree theory (EDT) on multiplex networks. We will show that predictions obtained from the EDT have excellent agreement with Monte Carlo simulations. Moreover, since the dynamics on multiplex networks involve more dynamical variables, which may invoke more computations, to reduce the computational burden, we further develop an approach based on partial effective degree theory (PEDT) for analyzing the dynamics on multiplex networks, where one layer adopts EDT and the other layer adopts the HMF. Our results show that PEDT has a good performance in predicting the target dynamical process.

Signal detection is generally related to network structure in both biological and engineering systems, and enormous effort has been putting into understanding the mechanism of amplification of weak signals in the aspects of self-tuning and scale-free topology. Here, we show that a third way of signal amplification exists, which does not require the scale-free topology as a necessary condition. This approach can effectively amplify the signal at an arbitrary node in a complex network by adaptively adjusting the coupling weights between the signal node and its neighbors, and thus can be used in both the local and global areas of a complex network. A theory is provided to explain its mechanism.

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