Diffusion processes are central to human interactions. Despite extensive studies that span multiple disciplines, our knowledge is limited to spreading processes in non-substitutive systems. Yet, a considerable number of ideas, products and behaviors spread by substitution-to adopt a new one, agents must give up an existing one. Here, we find that, ranging from mobile handsets to automobiles to smart phone apps, early growth patterns in substitutive systems follow a power law with non-integer exponents, in sharp contrast to the exponential growth customary in spreading phenomena. Tracing 3.6 million individuals substituting for mobile handsets for over a decade, we uncover three generic ingredients governing substitutive processes, allowing us to develop a minimal substitution model, which not only predict analytically the observed growth patterns, but also collapse growth trajectories of constituents from rather diverse systems into a single universal curve. These results demonstrate that the dynamics of complex substitutive systems are governed by robust self-organizing principles that go beyond the particulars of individual systems, which implies that these results could guide the understanding and prediction of all spreading phenomena driven by substitutions, from electric cars to scientific paradigms, from renewable energy to new healthy habits.
Universal Scaling in Complex Substitutive Systems
Ching Jin, Chaoming Song, Johannes Bjelland, Geoffrey Canright, Dashun Wang