title: Interacting branching process as a simple model of innovation.
abstract: We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/τ at each generation. In contrast with mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For τ = ∞, surviving processes exhibit a bottleneck before exploding superexponentially-a growth consistent with a law of accelerating returns. This behavior persists for finite τ. We analyze, in detail, the asymptotic behavior as p→0.
authors.affiliation: University of Calgary, Canada.
authors.forename: Vishal
authors.initials: V
authors.lastname: Sood
authors.forename: Myléne
authors.initials: M
authors.lastname: Mathieu
authors.forename: Amer
authors.initials: A
authors.lastname: Shreim
authors.forename: Peter
authors.initials: P
authors.lastname: Grassberger
authors.forename: Maya
authors.initials: M
authors.lastname: Paczuski