Model of macroeconomic evolution in stable regionally dependent economic fields

We develop a model for the evolution of economic entities within a geographical type of framework. On a square symmetry lattice made of three (economic) regions, firms, described by a scalar fitness, are allowed to move, adapt, merge or create spin-offs under predetermined rules, in a space and time dependent economic environment. We only consider here one timely variation of the ''external economic field condition''. For the firm fitness evolution we take into account a constraint such that the disappearance of a firm modifies the fitness of nearest neighboring ones, as in Bak-Sneppen population fitness evolution model. The concentration of firms, the averaged fitness, the regional distribution of firms, and fitness for different time moments, the number of collapsed, merged and new firms as a function of time have been recorded and are discussed. Also the asymptotic values of the number of firms present in the three regions together with their average fitness, as well as the number of respective births and collapses in the three regions are examined. It appears that a sort of $critical$ selection pressure exists. A power law dependence, signature of self-critical organization is seen in the birth and collapse asymptotic values for a high selection pressure only. A lack of self-organization is also seen at region borders.