2012/04/11 by A. Hernando, Alberto Hernando, A. Plastino
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · Psychology · #Applied mathematics #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Component (thermodynamics) #Computer science #Constraint (computer-aided design) #Demography #Formalism (music) #Logistic function #Logistic regression #Machine learning #Mathematics #Opinion Dynamics and Social Influence #Physics #Popularity #Population #Predictability #Psychology #Sociology #Statistical physics #Statistics #Theoretical computer science #cs.SI #physics.soc-ph #stat.AP
paper · pdf · doi:10.1016/j.physleta.2012.10.054
arxiv created 2012/04/11 · openalex publication_date 2012/11/13 · arxiv updated 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
On the basis of dynamical principles we derive the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way. So as to assess the predictability-power of our present formalism, we advance a prediction, regarding the next 60 months, for the number of users of the three main web browsers (Explorer, Firefox and Chrome) popularly referred as "Browser Wars".