Interacting branching process as a Simple model of innovation

TY - JOUR

T1 - Interacting branching process as a Simple model of innovation

AU - Sood, Vishal

AU - Mathieu, Mylene

AU - Shreim, Amer

AU - Grassberger, Peter

AU - Paczuski, Maya

PY - 2010/10/18

Y1 - 2010/10/18

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.105.178701

DO - 10.1103/PhysRevLett.105.178701

M3 - Journal article

SN - 0031-9007

VL - 105

SP - 178701

JO - Physical Review Letters

JF - Physical Review Letters

IS - 17

ER -