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An anticipatory extension of Malthusian model

2005-08-13
Akhmet, Marat
Öktem, Hüseyin Avni
Pickl, S. W.
Weber, Gerhard Wilhelm
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).