2011/04/30 by P. L. Krapivsky, S. Redner, D. Volovik +1
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Abandonment (legal) #Biology #Complex Network Analysis Techniques #Computer science #Demography #Function (biology) #Innovation Diffusion and Forecasting #Lambda #Law #Mathematical analysis #Mathematics #Monotonic function #Opinion Dynamics and Social Influence #Physics #Political science #Population #Quantum mechanics #Sociology #Transient (computer programming) #cond-mat.stat-mech #cs.SI #physics.soc-ph
paper · pdf · doi:10.1088/1742-5468/2011/12/p12003
published as J. Stat. Mech. P12003, (2011) · 4 pages, 2 columns, 5 figures, revtex 4-1 format; revised version has been expanded and put into iop format, with one figure added
arxiv created 2011/09/29 · openalex publication_date 2011/12/07 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose kinetic models for the spread of permanent innovations and\ntransient fads by the mechanism of social reinforcement. Each individual can be\nin one of M+1 states of awareness 0,1,2,...,M, with state M corresponding to\nadopting an innovation. An individual with awareness k<M increases to k+1 by\ninteracting with an adopter. Starting with a single adopter, the time for an\ninitially unaware population of size N to adopt a permanent innovation grows as\nln(N) for M=1, and as N1-1/M for M>1. The fraction of the population that\nremains clueless about a transient fad after it has come and gone changes\ndiscontinuously as a function of the fad abandonment rate lambda for M>1. The\nfad dies out completely in a time that varies non-monotonically with lambda.\n