We assume that the primary growth for the lynx population depends on sufficient food for raising lynx kittens, which implies an adequate source of nutrients from predation on hares. Thus, the growth of the lynx population does not only depend of how many lynx there are, but on how many hares they can eat. In a time interval \( \Delta t HL \) hares and lynx can meet, and in a fraction \( b\Delta t HL \) the lynx eats the hare. All of this does not contribute to the growth of lynx, again just a fraction of \( b\Delta t HL \) that we write as \( d\Delta t HL \). In addition, lynx die just as in the population dynamics with one isolated animal population, leading to a loss \( -c\Delta t L \).

The accounting of lynx then looks like $$ \Delta L = d\Delta t H^nL^n - c\Delta t L^n$$