Controlling self-organized criticality in sandpile models

Abstract

We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action, which amounts to triggering avalanches in sites that are near to be come critical, reduces the probability of very large events, so that energy dissipation occurs most locally. The control is applied to a directed Abelian sandpile model driven by both uncorrelated and correlated deposition. The latter is essential to design an efficient and simple control heuristic, but has only small influence in the uncontrolled avalanche probability distribution. The proposed control seeks a tradeoff between control cost and large event risk. Preliminary results hint that the proposed control works also for an undirected sandpile model.

Controlling self-organized criticality in complex networks

“…It is intuitive that, if p H is decreased, the controller is less efficient to reduce the chance of large avalanches, but smaller p H are clearly more economical. This can be seen in the small s region of the inset of Fig.1, where the number of small avalanches of the controlled system with p H = 0.05 is smaller than that with p H = 0.1. p H plays a role similar to the acceptable size a c considered in [15]. Two costs are of relevance in this control scheme, namely the cost of scanning the high degree nodes in order to see if they are saturated and the cost of the intervention (explosion).…”

“…Here, differently from [15], the control scheme does not depend on the replica model and, therefore, is less costly than the one presented in [15]. Furthermore, while in [15] we were interested in controlling the size of avalanches in only a region of the system, in this paper we are interested in controlling the size of the avalanches in the whole network.…”

“…In that paper, we have shown that an external control action, which amounts to triggering avalanches in sites that are near to be come critical, was able to reduce the probability of very large events, so that mass dissipation occurs most locally. Due to the homogeneity of the lattice where traditional SOC phenomena have been investigated, one difficult present in [15] is that, in order to make the decision whether an avalanche should or not be exogenously triggered, one had to simulate a replica model of the region of the system to be controlled. Here, differently from [15], the control scheme does not depend on the replica model and, therefore, is less costly than the one presented in [15].…”

“…Due to the homogeneity of the lattice where traditional SOC phenomena have been investigated, one difficult present in [15] is that, in order to make the decision whether an avalanche should or not be exogenously triggered, one had to simulate a replica model of the region of the system to be controlled. Here, differently from [15], the control scheme does not depend on the replica model and, therefore, is less costly than the one presented in [15]. Furthermore, while in [15] we were interested in controlling the size of avalanches in only a region of the system, in this paper we are interested in controlling the size of the avalanches in the whole network.…”

Robot traders can prevent extreme events in complex stock markets

“…Although economists are hardly prepared to recognize this fact [3], here one has to resort to the control theory of self-organized systems [4]. Collective behavior based on self-organization has been shown in animals living in groups as well as in humans.…”