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Permanence of population growth models with impulsive effects. (English) Zbl 1185.34014
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.

34A37Differential equations with impulses
92D25Population dynamics (general)
Full Text: DOI
[1] Angelova, J.; Dishliev, A.: Optimization problems for impulsive models from population dynamics. (1994) · 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.: Proceedings of the American mathematical society. 96, 425-430 (1986)
[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) · 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