An anticipatory extension of Malthusian model

AKHMET M., ÖKTEM H. A., Pickl S. W., WEBER G. W.

7th International Conference on Computing Anticipatory Systems (CASYS 05), Liege, Belgium, 8 - 13 August 2005, vol.839, pp.260-262 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 839
  • City: Liege
  • Country: Belgium
  • Page Numbers: pp.260-262
  • Keywords: the Malthusian model, strong anticipation, stability, piecewise constant argument, DIFFERENTIAL-EQUATIONS, SYSTEMS
  • Middle East Technical University Affiliated: Yes


In this paper, on the base of a new variable - deviation of population from an average value, we propose a new extension of the Malthusian model (see equations (10), (15) and (20)) using differential equations with piecewise constant argument which can be retarded as well as advanced. We study existence of periodic solutions and stability of the equations by method of reduction to discrete equations [4]. Equations (15) and (20) with advanced argument are systems with strong anticipation [6, 7]. Moreover, we obtain a new interpretation of known results for differential equations with piecewise constant argument (6) and (8).