Emergence of Scaling in Complex Substitutive Systems

TL;DR

This paper reveals that substitution-driven diffusion processes across various domains exhibit power-law early growth patterns, challenging the exponential growth assumption and uncovering universal self-organizing principles.

Contribution

It introduces a minimal substitution model explaining power-law growth and unifies diverse substitution dynamics under a common mechanistic framework.

Findings

Power-law early growth observed in multiple domains.

A minimal substitution model explains the universal growth pattern.

Substitution dynamics governed by robust self-organizing principles.

Abstract

Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles, from smart-phone 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 analyzing a unique data tracing 3.6M individuals substituting for 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.