Liu, Xinzhi; Shen, Xuemin Impulsive stabilization and application to a population growth model. (English) Zbl 1055.34012 Nonlinear Dyn. Syst. Theory 2, No. 2, 173-184 (2002). 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. Reviewer: Vigirdas Mackevičius (Vilnius) 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) Keywords:impulsive stabilization; control; population growth model PDFBibTeX XMLCite \textit{X. Liu} and \textit{X. Shen}, Nonlinear Dyn. Syst. Theory 2, No. 2, 173--184 (2002; Zbl 1055.34012)