Interacting branching process as a simple model of innovation |
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Authors: | Sood Vishal Mathieu Myléne Shreim Amer Grassberger Peter Paczuski Maya |
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Institution: | University of Calgary, Canada. |
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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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