In this paper, we design a greedy routing on networks of mobile agents. In the greedy routing algorithm, every time step a packet in agent $i$ is delivered to the agent $j$ whose distance from the destination is shortest among searched neighbors of agent $i$. Based on the greedy routing, we study the traffic dynamics and traffic-driven epidemic spreading on networks of mobile agents. We find that the transportation capacity of networks and the epidemic threshold increase as the communication radius increases. For moderate moving speed, the transportation capacity of networks is the highest and the epidemic threshold maintains a large value. These results can help controlling the traffic congestion and epidemic spreading on mobile networks.
Sun et al. provided an insightful comment arXiv:1108.5739v1 on our manuscript entitled Controllability of Complex Networks with Nonlinear Dynamics on arXiv. We agree on their main point that linearization about locally desired states can be violated in general by the breakdown of local control of the linearized complex network with nonlinear state. Therefore, we withdraw our manuscript. However, other than nonlinear dynamics, our claim that a single-node-control can fully control the general bidirectional/undirected linear network with 1D self-dynamics is still valid, which is similar to (but different from) the conclusion of arXiv:1106.2573v3 that all-node-control with a single signal can fully control any direct linear network with nodal-dynamics (1D self-dynamics).
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
