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Impulsive control of a Lotka-Volterra system. (English) Zbl 0949.93069

The following Lotka-Volterra population growth model

N ˙ 1 =N 1 (b 1 +a 11 N 1 +a 12 N 2 +a 13 N 3 )N ˙ 2 =N 2 (b 2 +a 21 N 1 +a 22 N 2 +a 33 N 3 )N ˙ 3 =N 3 (b 3 +a 31 N 1 +a 32 N 2 +a 33 N 3 )

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:
93D15Stabilization of systems by feedback
92D25Population dynamics (general)