A MATHEMATICAL PATTERN OF THE RELATION MAN-ENVIRONMENT, REPRESENTED BY ANTICIPATORY SYSTEMS

In a pair of mixed advanced-retarded differential equations we consider man as being the master system and the environment as the slave system. This is the case when man’s behaviour is dependent on a future state of the environment, while the environment’s rate of change is dependent on a past state (hence a past action) of man. Man, as the master system, should take forecasts into consideration. The mathematical model used in the paper pertains to the modelling of interaction of two systems, such as the observation operator, the pragmatic operator, and especially the differential system of equations, in case the reciprocal influence between two systems manifests itself, throughout their evolution, with a time difference.