Ballinger, G.; Liu, X. Permanence of population growth models with impulsive effects. (English) Zbl 1185.34014 Math. Comput. Modelling 26, No. 12, 59-72 (1997). Summary: This paper establishes criteria for permanence of populations which undergo impulsive effects at fixed times between intervals of continuous evolution governed by a differential system. It is also shown that suitable impulses may prevent the extinction or unbounded growth of populations whose evolutions are otherwise governed solely by a differential system. Examples are provided to demonstrate the application of the results obtained. Cited in 107 Documents MSC: 34A37 Ordinary differential equations with impulses 92D25 Population dynamics (general) PDF BibTeX XML Cite \textit{G. Ballinger} and \textit{X. Liu}, Math. Comput. Modelling 26, No. 12, 59--72 (1997; Zbl 1185.34014) Full Text: DOI OpenURL References: [1] Angelova, J.; Dishliev, A., Optimization problems for impulsive models from population dynamics, (1994), Manuscript, Bulgaria · Zbl 0942.34010 [2] Liu, X.Z., Stability results for impulsive differential systems with applications to population growth models, Dynamics and stability of systems, 9, 163-174, (1994) · Zbl 0808.34056 [3] Butler, G.; Freedman, H.I.; Waltman, P., (), 425-430 [4] Gard, T., Uniform persistence in multispecies populations, Mathematical biosciences, 85, 93-104, (1987) · Zbl 0631.92012 [5] Zanolin, F., Permanence and positive periodic solutions for Kolmogorov competing species systems, Results in mathematics, 21, 224-250, (1992) · Zbl 0765.92022 [6] Lakshmikantham, V.; Bainov, D.D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific Singapore · Zbl 0719.34002 [7] Liu, X.Z., Further extensions of the direct method and stability of impulsive systems, Nonlinear world, 1, 341-354, (1994) · Zbl 0809.34066 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.