Robustness of Controllability for Scale-free Networks Based on a Nonlinear Load-Capacity Model**This work is supported by the National Natural Science Foundation of China under Grant Nos. 61374053 and 61473016, HKU Conference and Research Council under Grant 201411159037, and the Fundamental Research Funds for the Central Universities YWF-15-ZDHXY-001.

Abstract

Abstract Based on a nonlinear load-capacity model, the network evolution and controllability evolution of scale-free networks under the cascading failures triggered by removing the highest-load edge are simulated and discussed in this paper. It is shown by numerical simulations that the controllability evolution is consistent with the average degree evolution rather than the power law exponent evolution. Under the same network cost, it is found that the nonlinear load-capacity model exhibits the stronger robustness of controllability when the initial power law exponent of networks is small by comparing with the linear load-capacity model, while the linear load-capacity model is of stronger robustness of controllability when the initial power law exponent is large. Numerical results shows that high-load edges are becoming more critical to the robustness of controllability with the increase of initial power law exponent, and the nearly highest-load edges are becoming more critical with the increase of both initial average degree and power law exponent.