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Center for Nonlinear Studies |
We investigate a class of models related to the Bak-Sneppen model, initially proposed to study evolution. In this model random variables in $[0,1]$ (random fitnesses) are associated to a number of agents, located at the vertices of a graph $G$. Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others (with a priori given rank probabilities) are replaced by new agents with random fitnesses. We consider two cases: The exogenous case where the new fitnesses are taken from an a priori fixed distribution, and the endogenous case where the new fitnesses are taken from the current distribution as it evolves. We formulate an approximate theory (Rank-Driven dynamics) that allows to essentially exactly solve the underlying dynamics.
Host: Pieter Swart