Avalanche dynamics is an indispensable feature of complex systems. Here, we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent through the Bak–Tang–Wiesenfeld (BTW) sandpile model. The threshold height of a node i is set as k1− i with 06 ¡ 1, where ki is the degree of node i. Using the branching process approach, we obtain the avalanche size and...

We study the abelian avalanche model, an analogue of the abelian sandpile model with continuous heights, which allows for arbitrary small values of dissipation. We prove that for non-zero dissipation, the infinite volume limit of the stationary measures of the abelian avalanche model exists and can be obtained via a weighted spanning tree measure. Moreover we obtain exponential decay of spatial...

We study the avalanche dynamics in the data-packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with the proportionality constant 1+a . When the system is perturbed by a single vertex removal, the load of each vertex is redistributed, followed by subsequent failures of overloaded vertices. The avalanche size d...

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd ðkÞ k ; through the Bak–Tang–Wiesenfeld sandpile model. The threshold height of a node i is set to be k 1 Z i with 0pZo1: We obtain the exponents for the avalanche size and the duration distributions analytically as a function of g and Z by using the branching process approach. The analytic solutio...