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Phys Rev Lett. 2010 Oct 22;105(17):178701. Epub 2010 Oct 18.

Interacting branching process as a simple model of innovation.

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1
University of Calgary, Canada.

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.

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