Research On The Influence Of Driving Mechanism And Network Topology On The Avalanche Dynamics On Complex Networks

Complex networks and Self-Organized Criticality (SOC) have very close connection. In this paper, we mainly studied several problems on the avalanche dynamics on complex networks which exhibits the Self-Organized Criticality as follows: the universality class of the stochastic sandpile model, the influence of assortative mixing on sandpile avalanche dynamics on complex networks, the influence of driving mechanism on sandpile avalanche dynamics on complex networks. In addition, we also studied the weak hit strategy on complex networks.Firstly, in order to investigate whether the Abelian symmetry breaking changes the universality class of the stochastic sandpile model, we numerically studied the avalanche behavior of non-Abelian stochastic sandpile model. Avalanches can be separated into dissipative avalanches and nondissipative avalanches. Most of the previous researches did not study dissipative and nondissipative avalanches separately. In this paper, we investigated the distributions of dissipative and nondissipative avalanches separately in the non-Abelian stochastic sandpile model in two dimensions. We found that dissipative and nondissipative avalanche distributions have difference as well as identity. Both of dissipative and nondissipative avalanche distributions obey simple power laws under the finite-size scaling and do not have the logarithmic correction. However, we also found that dissipative and nondissipative avalanche distributions have different critical exponents, which means that they exhibit different scaling behavior.Compared with correlative results of Abelian stochastic sandpile model studied in recent reference, dissipative and nondissipative avalanche distributions of non-Abelian stochastic sandpile model was found not to include a logarithmic correction, while dissipative and nondissipative avalanche distributions of Abelian stochastic sandpile model need to include a logarithmic correction. We also found that critical exponents of dissipative and nondissipative avalanches in non-Abelian stochastic sandpile model are different from the corresponding values in the Abelian stochastic sandpile model respectively. All these indicate that the non-Abelian stochastic sandpile model and the Abelian stochastic sandpile model belong to distinct universality classes, which imply that the Abelian symmetry breaking changes universality class of the stochastic sandpile model.In order to investigate how the network topology influences the dynamic behavior, we numerically studied the influence of assortative mixing on sandpile avalanche dynamics on scale-free networks. Assortative mixing is an important characteristic which describes the correlation that high-degree nodes prefer to be connected to other high-degree nodes. It is observed that a large fraction of multiple topplings are included in avalanches on assortative networks, which is absent on uncorrelated networks. Unlike the case on uncorrelated networks, the distributions of avalanche size, area and duration do not follow pure power law, but deviate more obviously from pure power law with the growing degree of assortativity. This may result from the fact that the increasing degree of assortativity can cause the emergence of clusters in the network where nodes with the same degree connect with each other. The increasing degree of assortativity changes the structure of the uncorrelated scale-free network from complete heterogeneity into local-homogeneity and thus causes the appearance of a large fraction of multiple topplings, leading to the destruction of the critical behavior of the avalanche process. The results showed that the behavior of avalanche dynamics on scale-free networks does not only depend on the degree distribution of the network, but also is strongly influenced by the assortative mixing of the network.The influence of driving mechanism of sandpile model is a very important problem in the research of Self-Organized Criticality. The sandpile model on complex networks is a classic model which exhibits the Self-Organized Criticality. Aiming to understand how the driving mechanism influences the avalanche dynamics on complex networks, we introduced a new sandpile model driven by degree on scale-free networks where the perturbation is randomly triggered at nodes with the same degree. We numerically investigated the avalanche behavior of sandpile driven by different degrees on scale-free networks. It was found that the avalanche distribution obeys the pure power low only when the sandpile is driven at nodes with the minimal degree. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually violates the clean power law and the critical behavior of the system is destroyed. This may results from the fact that the number of larger avalanches increases and the number of smaller avalanches decreases with the growing degree of the driven nodes. Thus, when the number of larger avalanches exceeds the number of smaller avalanches, the power-law avalanche distribution is destroyed. The results also showed that the average avalanche area increases with the degree of driven nodes. This indicates that perturbation triggered on higher-degree nodes may result in broader spreading of avalanche propagation.However, the precise measure to the network topology may not be available in real cases, but the relative values of characteristic properties in a network such as ranks are easy to obtain. Under this consideration, on the basis of the sandpile model driven by degree, we proposed another new sandpile model driven by ranking on scale-free network. In this model each node has a drive probability which only depends on the rank of thenode's degree and a dynamical parameterβis introduced to characterize theununiformity of drive probability in the network. We numerically simulated this model on BA scale-free network and found that the increasing ununiformity of drive probability causes the decreasing ununiformity of avalanche distribution, which finally leads to the destruction of the critical behavior of the system. The power spectrum of the system is also investigated and discovered to exhibit weak long-range temporal correlation underdifferent dynamical parameterβ. This indicates that the quasi-disordered driving mechanism may induce the weakly long-range temporal correlated response.In addition, we also numerically studied the weak hit strategy on complex networks. The weak hit strategy does not lead to the complete inactivation of a single target, but induces a partial inactivation of multiple targets. We also introduced a new continuous weak hit strategy on complex networks and used a parameterωto define the hit intensity. For the weak hit strategy introduced by previous research, our results showed that weak hits of multiple targets may produce a higher effect than the complete knockout of a single target on both scale-free network and random network. For the continuous weak hit strategy, our results showed that the continuous weak hits on two selected nodes with small hit intensityωcould achieve the same damage of complete elimination of a single selected node on both scale-free network and random networks. It was also found that the continuous weak hits on a single selected edge with smallωcan reach the same effect of complete elimination of a single edge on scale-free network, but on random network the damage of the continuous weak hits on a single edge is close to but always smaller than that of complete elimination of a single edge even ifωis very large. All these indicate that multiple weak hits and multiple continuous weak hits may be more effective than complete knockout of a single target on complex networks if the suitable weak hit strategy is chosen.