Power Law Scaling for a System of Interacting Units with Complex Internal Structure

Abstract

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.

4 pages with 4 postscript figures (uses Revtex 3.1, Latex2e, multicol.sty, epsf.sty and rotate.sty). Submitted to PRL

References in corpus (1)

• Scaling behavior in economics: II. Modeling of company growth

Cited by in corpus (64)

• Universal and non-universal properties of cross-correlations in financial time series
• The statistical properties of the volatility of price fluctuations
• Scaling of the distribution of price fluctuations of individual companies
• Fluctuation scaling in complex systems: Taylor's law and beyond
• Universal features in the growth dynamics of complex organizations
• Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms
• The Growth of Business Firms: Theoretical Framework and Empirical Evidence
• On Universality in Human Correspondence Activity
• Languages cool as they expand: Allometric scaling and the decreasing need for new words
• Volatility clustering and scaling for financial time series due to attractor bubbling
• Ivory Tower Universities and Competitive Business Firms
• Self-Organized Segregation within an Evolving Population
• The Extreme Risk of Personal Data Breaches & The Erosion of Privacy
• Growth and Fluctuations of Personal Income
• Microdynamics in stationary complex networks
• Statistical Laws Governing Fluctuations in Word Use from Word Birth to Word Death
• Universality of Zipf's Law
• The Size Variance Relationship of Business Firm Growth Rates
• A Triple Helix Model of Medical Innovation: Supply, Demand, and Technological Capabilities in terms of Medical Subject Headings
• Zipf Law in Firms Bankruptcy
• Scaling laws in the dynamics of crime growth rate
• Statistical Properties of Business Firms Structure and Growth
• Generic Emergence of Power Law Distributions and Lévy-Stable Intermittent Fluctuations in Discrete Logistic Systems
• Power-Law Population Heterogeneity Governs Epidemic Waves
• Election turnout statistics in many countries: similarities, differences, and a diffusive field model for decision-making
• Bipartite Producer-Consumer Networks and the Size Distribution of Firms
• Minority game with arbitrary cutoffs
• Pareto index induced from the scale of companies
• Generalised central limit theorems for growth rate distribution of complex systems
• Derivation of the distribution from extended Gibrat's law
• Annual change of Pareto index dynamically deduced from the law of detailed quasi-balance
• Extinction events and species lifetimes in a simple ecological model
• The uniqueness of company size distribution function from tent-shaped growth rate distribution
• A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment
• Non-Markov stochastic dynamics of real epidemic process of respiratory infections
• Innovation flow through social networks: Productivity distribution
• A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence
• Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients
• Long-term evolution of email networks: Statistical regularities, predictability and stability of social behaviors
• Fat-tailed fluctuations in the size of organizations: the role of social influence
• Communication activity in social networks: growth and correlations
• Surface roughness analysis of the hydrophilic SiO_2/TiO_2 nano bi-layers by Level crossing approach
• Evolutionary freezing in a competitive population
• Control of silver-polymer aggregation mechanism by primary particle spatial correlations in dynamic fractal-like geometry
• The Production Function
• Stochastic dynamics and the predictability of big hits in online videos
• Competition and fragmentation: a simple model generating lognormal-like distributions
• Exploitation dynamics of fish stocks
• Temporal Taylor's scaling of facial electromyography and electrodermal activity in the course of emotional stimulation
• Physics of Econophysics
• Evolutionary Model of the Growth and Size of Firms
• A simple model for the formation of a complex organism
• The Italian primary school-size distribution and the city-size: a complex nexus
• The cause of universality in growth fluctuations
• On the growth of primary industry and population of China's counties
• Firms Growth Dynamics, Competition and Power Law Scaling
• Emergent organization in a model market
• A 2D Levy-flight model for the complex dynamics of real-life financial markets
• Universal fluctuations in growth dynamics of economic systems
• Continuum rich-get-richer processes: Mean field analysis with an application to firm size
• Is it a power law distribution? The case of economic contractions
• Bankruptcy as an exit mechanism for systems with a variable number of components
• Scaling in the growth of geographically subdivided populations: invariant patterns from a continent-wide biological survey
• R&D Strategy Document