Scale-invariance underlying the logistic equation and its social applications

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) 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 a 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.

► Scale-invariance and mean-value are sufficient and necessary conditions for the LE.
► We generalize the LE to multi-component systems, and find the analytical result.
► We show that it underlies interesting empirical social processes.
► Examples: city-populations, diffusion in networks, and popularity of tech-products.
► Prediction: regarding the next 5 years, for the number of users of Net Browsers.