Matematické Fórum

Skrytý text:


The numbers od foxes (l) and hares (z) in the woods are described by the above mentioned system of differential equations.

According to the wildlife census, the hares are overpopulated due to a mild winter. Hence, thanks to the sufficiency of feed there is a risk that the foxes will prevail and eat most of the hares resulting in the collapse of the whole system. There is hares and foxes in the woods at the moment. What minimal counts can they both achieve under the current state? How many hares have to be caught by the hunters so that the number of foxes in the woods will never drop below 50?  (Neglect all external influences like a repetition of mild winter or, conversely, cold winter.)