The demographic situation simulation in the region in view of the phenomenon of hysteresis
Most models of complex systems linking the exogenous and endogenous factors based on GMDH-simulations do not take into account the processes related to the inertia of a complex system determined by the effect of the lag - system reaction lag to any exogenous (external) factor. The complexity of this task is that the correct lag accounting requires time series with sufficient duration, which is not possible to resolve when a number of forecasting problems in complex systems, in particular, demographic studies are solved. For such task solution the three-layer dynamic structural-functional model, linking the exogenous and endogenous factors in the socio-economic system in view of the time-lags, is proposed. The first layer of the model generates a lot of GMH type static models. Neural network structures are used for realization of GMH-models. The difference of the proposed GMDH neural network is that each block nonlinear static model of the first layer is a GMDH neural network on inputs of which models received by GMDH-simulation, incorporating many endogenous and exogenous factors, are entered. The second layer is a linear dynamic model. Linear dynamic model building process with distributed lags is developed on the basis of a method of Almon. Dynamic models of endogenous factors and vector of exogenous factors exist on models inputs of the third layer. Taking into account that the setting of each layer of the model goes offline, the vectors of equal length enter inputs of the third layer model block. Input vector consists of two components. The feature that defines the endogenous factors is determined in the second layer. The feature that defines the exogenous factors, is set or planned by the decision-maker.