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Impulsive stabilization and application to a population growth model. (English) Zbl 1055.34012

For a system of autonomous ordinary differential equations, the authors establish necessary and sufficient conditions for a given state (not necessarily an equilibrium point) to be impulsively stabilizable. The results are applied to a three-species fish population growth model. An impulsive control program is constructed. It shows that by impulsive regulation of one species one can maintain all three species at a positive level, which, otherwise, would drop to a level of extinction for one of the species.

MSC:

34A37 Ordinary differential equations with impulses
34D20 Stability of solutions to ordinary differential equations
93B05 Controllability
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
93D21 Adaptive or robust stabilization
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
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