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Impulsive control of a Lotka-Volterra system. (English) Zbl 0949.93069
The following Lotka-Volterra population growth model \align \dot N_1 & =N_1(b_1+a_{11} N_1+a_{12} N_2+a_{13}N_3)\\ \dot N_2 & =N_2(b_2+a_{21} N_1+a_{22} N_2+a_{33} N_3)\\ \dot N_3 & =N_3(b_3+a_{31} N_1+ a_{32}N_2+ a_{33}N_3) \endalign where $a_{ij}$ and $b_i$ $i,j=1,2,3$ are constants is considered. The dynamics of the processes is controlled via impulses of the $N_1$ process. At selected impulse instants, it is possible to switch the process to a new state. With this impulsive control the question is if it is possible to keep the processes $N_1$, $N_2$, $N_3$ from going extinct by stabilizing some positive point. Some stabilizability criteria are given and several examples are worked out.

MSC:
 93D15 Stabilization of systems by feedback 92D25 Population dynamics (general)
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