Theoretical results for sandpile models of self-organized criticality with multiple topplings

We study a directed stochastic sandpile model of self-organized criticality, which exhibits multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the steady-state all stable states are equally likely. Using this fact, we explicitly derive a discrete dynamical equation for avalanches on the lattice. By coarse graining we arrive at a continuous Langevin equation for the propagation of avalanches and calculate all the critical exponents characterizing avalanches. The avalanche equation is similar to the Edwards-Wilkinson equation, but with a noise amplitude that is a threshold function of the local avalanche activity, or interface height, leading to a stable absorbing state when the avalanche dies.

Self-organized networks of competing boolean agents

A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest player's strategy is changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths.