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

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.