A model of coupled maps for economic dynamics

Abstract

An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control term representing the local environmental pressure which avoids an exponential growth. The asymptotic state of the system evolution displays a complex behavior. The distribution of the maps values in this final regime is of power law type. In the model, inequality emerges as a result of the dynamical processes taking place in the microscopic scales.Key words: coupled-maps models, non-equilibrium systems, power law scaling Inequality in the richness distribution is a fact in each economic activity. The origin of such behavior seems to be caused by the interaction of the macro with the microeconomy. Here we propose a simple spatio-temporal model for economy evolution where inequality emerges as a result of the dynamical processes taking only place on the microscopic scale. That is, the microeconomy fully determines the macroeconomic characteristics of the system. The model is composed by N interacting agents representing a company, country or other economic entity. Each agent, identified by an index i = 1 · · · N, is characterized by a real, scalar degree of freedom, x i ∈ [0, ∞] denoting the strength, wealth or richness of the agent. The system evolves in time t synchronously. Each agent updates its x t i value according to its present state and

Pareto and Boltzmann–Gibbs behaviors in a deterministic multi-agent system

“…Although the model can be defined on any network of interacting agents, for simplicity we shall consider here a one-dimensional lattice with periodic boundary conditions. The dynamics of the system is described by the coupled map equations [12] …”

Exponential or Power Law? How to Select a Stable Distribution of Probability in a Physical System

“…where Π z=0 ≡ Π q =1 = Π q=1 , z ≡ q − 1 = 1 − q and 0 ≤ z < 1 as 0 < q ≤ 1. Together, equations (19), (20), (21) and (22) allow computation of Π z (hence, of Π q ) once A (u) and D are known.…”

Competitively coupled maps and spatial pattern formation

“…Although the model studied in these papers is formally similar to our model, the aims of our work and that of Refs. [20][21][22] are very different. Whereas our focus is on how a homogeneous initial state can undergo spontaneous symmetry breaking and result in stable pattern formation, Refs.…”

“…[20][21][22] in the context of understanding income distributions. Although the model studied in these papers is formally similar to our model, the aims of our work and that of Refs.…”

“…Whereas our focus is on how a homogeneous initial state can undergo spontaneous symmetry breaking and result in stable pattern formation, Refs. [20][21][22] do not contain any discussion of spatial pattern formation and are, instead, concerned with modeling wealth or income distributions in society.…”