A logistic map approach to economic cycles I. The best adapted companies

TL;DR

This paper models economic cycles using a logistic map approach, analyzing how environmental factors influence company fitness and population dynamics, revealing conditions for growth, decay, and chaotic behavior.

Contribution

It introduces a birth-death lattice gas model mapped onto a high-order logistic map to analytically study economic entity dynamics and cycles.

Findings

Identifies conditions for growth, decay, and stability in economic populations.

Shows bifurcations and chaotic solutions depend on business plan parameters.

Provides microscopic insights into economic cycling phenomena.

Abstract

A birth-death lattice gas model about the influence of an environment on the fitness and concentration evolution of economic entities is analytically examined. The model can be mapped onto a high order logistic map. The control parameter is a (scalar) "business plan". Conditions are searched for growth and decay processes, stable states, upper and lower bounds, bifurcations, periodic and chaotic solutions. The evolution equation of the economic population for the best fitted companies indicates "microscopic conditions" for cycling. The evolution of a dynamic exponent is shown as a function of the business plan parameters.