MODELING HARVESTING PROCESSES FOR POPULATIONS WITH NON-OVERLAPPING GENERATIONS

Difference equations are used in order to model the dynamics of populations with non-overlapping generations, since growth such occurs only at discrete points time. In simplest case have form $N_{t+1}= F(N_t)$, where $N_t >0$ is population size a moment time $t$, and $F$ smooth function. Among logistic equation Ricker's most often practice. given paper, these considered width taking into account an effect harvesting, that is, below studied $N_{t+1}=r N_t (1- N_t) - c$ \exp (r(1 / K )) c$, parameters $r$, $K>0$, $c>0$ harvesting intensity. Positive equilibrium conditions for their stability were found. These kinds states realized nature. For practice, periodic solutions also important, especially periods $T=2 (N_{t+2} = N_t)$ $T=3 (N_{t+3} N_t)$, since, existence, by Sharkovskii's theorem, one can do conclusions about existence other periods. analytical form, values make up solution period $T=2$ We numerical methods find $T=3$. model, question be investigated computer analysis only. number experiments conducted which found was studied. chaotic As we see, study difference gives many unexpected results.