Simple discrete-continuous models of the predator-prey system and a discrete second-order isolated population model

The paper considers a discrete-continuous model of the predator-prey system and a discrete model of an isolated population derived from it. Unlike the well-known Lotka-Volterra model, this model assumes that the generation of new individuals occurs at fixed points in time. Thus, the model is mathematically a system of differential equations with impulses. For the isolated population model derived from this system, as a second-order nonlinear difference equation, the dynamic regimes and phase rearrangements in the conservative and non-conservative case are studied. The relevance of the model is confirmed by good agreement with experimental data obtained from freely available databases of population abundances. Keywords.

УДК 517.9

Keywords: ODE with impulses, bifurcations of mappings, conservative dynamics, population dynamics, discrete-continuous models.