One dimensional stylized model taking into account spatial activity of firms with uniformly distributed customers is proposed. The spatial selling area of each firm is defined by a short interval cut out from selling space (large interval). In this r
epresentation, the firm size is directly associated with the size of its selling interval. The recursive synchronous dynamics of economic evolution is discussed where the growth rate is proportional to the firm size incremented by the term including the overlap of the selling area with areas of competing firms. Other words, the overlap of selling areas inherently generate a negative feedback originated from the pattern of demand. Numerical simulations focused on the obtaining of the firm size distributions uncovered that the range of free parameters where the Paretos law holds corresponds to the range for which the pair correlation between the nearest neighbor firms attains its minimum.
The influence of nonmagnetic central node defect on dynamical properties of regular square-shaped 5 x 5 segment of magnetic dot array under the thermal activation is investigated via computer simulations. Using stochastic Landau-Lifshitz-Gilbert equa
tion we simulate hysteresis and relaxation processes. The remarkable quantitative and qualitative differences between magnetic dot arrays with nonmagnetic central node defect and magnetic dot arrays without defects have been found.
