Anticipatory Systems in Population Dynamics

This paper deals with anticipatory systems and their use when describing the population dynamics of single species discrete systems. In doing so, it starts from Rosen's original definition of anticipatory system and its extending in the papers of Dubois. Then the concepts of incursion and hyperincursion are briefly explained and their applications to modeling discrete dynamic systems are outlined. A detailed analysis is given of the population model described by the first order difference equation, where the relative population size at future time is a cubic polynomial function of the population size at the present. Consequently, the corresponding in cursive and hyperincursive models are formulated and the stability of their equilibrium solutions (trajectories) is studied.