Emergence of scaling in complex substitutive systems

Ching Jin, Chaoming Song, Johannes Bjelland, Geoffrey Canright, Dashun Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Diffusion processes are central to human interactions. One common prediction of the current modelling frameworks is that initial spreading dynamics follow exponential growth. Here we find that, for subjects ranging from mobile handsets to automobiles and from smartphone apps to scientific fields, early growth patterns follow a power law with non-integer exponents. We test the hypothesis that mechanisms specific to substitution dynamics may play a role, by analysing unique data tracing 3.6 million individuals substituting different mobile handsets. We uncover three generic ingredients governing substitutions, allowing us to develop a minimal substitution model, which not only explains the power-law growth, but also collapses diverse growth trajectories of individual constituents into a single curve. These results offer a mechanistic understanding of power-law early growth patterns emerging from various domains and demonstrate that substitution dynamics are governed by robust self-organizing principles that go beyond the particulars of individual systems.

Original languageEnglish (US)
Pages (from-to)837-846
Number of pages10
JournalNature human behaviour
Issue number8
StatePublished - Aug 1 2019

ASJC Scopus subject areas

  • Social Psychology
  • Experimental and Cognitive Psychology
  • Behavioral Neuroscience


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