Cascading failures in coupled networks with both inner-dependency and inter-dependency links

We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We find that when most of dependency links are inner- or inter-ones, the coupled networks system is fragile and makes a discontinuous percolation transition. However, when the numbers of two types of dependency links are close to each other, the system is robust and makes a continuous percolation transition. This indicates that the high density of dependency links could not always lead to a discontinuous percolation transition as the previous studies. More interestingly, although the robustness of the system can be optimized by adjusting the ratio of the two types of dependency links, there exists a critical average degree of the networks for coupled random networks, below which the crossover of the two types of percolation transitions disappears, and the system will always demonstrate a discontinuous percolation transition. We also develop an approach to analyze this model, which is agreement with the simulation results well.Comment: 9 pages, 4 figure

Parameter-tuning Networks: Experiments and Active Walk Model

The tuning process of a large apparatus of many components could be represented and quantified by constructing parameter-tuning networks. The experimental tuning of the ion source of the neutral beam injector of HT-7 Tokamak is presented as an example. Stretched-exponential cumulative degree distributions are found in the parameter-tuning networks. An active walk model with eight walkers is constructed. Each active walker is a particle moving with friction in an energy landscape; the landscape is modified by the collective action of all the walkers. Numerical simulations show that the parameter-tuning networks generated by the model also give stretched exponential functions, in good agreement with experiments. Our methods provide a new way and a new insight to understand the action of humans in the parameter-tuning of experimental processes, is helpful for experimental research and other optimization problems.Comment: 4 pages, 5 figure