Wang, Fengyan; Pang, Guoping; Chen, Lansun Qualitative analysis and applications of a kind of state-dependent impulsive differential equations. (English) Zbl 1146.34006 J. Comput. Appl. Math. 216, No. 1, 279-296 (2008). The authors investigate qualitative properties of a system of state-dependent impulsive differential equations. Several theorems for the existence of a periodic solution and for the stability are proved. As an application a stage-structure single population model with periodically impulsive adding and harvesting is studied. Reviewer: Gani T. Stamov (Sliven) Cited in 7 Documents MSC: 34A37 Ordinary differential equations with impulses 34D05 Asymptotic properties of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 92D25 Population dynamics (general) Keywords:impulsive semi-dynamical systems; \(k\)th-order periodic solution; asymptotic stability PDF BibTeX XML Cite \textit{F. Wang} et al., J. Comput. Appl. Math. 216, No. 1, 279--296 (2008; Zbl 1146.34006) Full Text: DOI References: [1] Angelova, J.; Dishliev, A., Optimal problem for one-impulsive models from population dynamics, Nonlinear anal., 39, 483-497, (2000) · Zbl 0942.34010 [2] Bainov, D.; Simeonov, P., Impulsive differential equations: periodic solutions and applications, (1989), Wiley New York · Zbl 0815.34001 [3] Bainov, D.D.; Simeonov, P.S., System with impulsive effect: stability, theory and equations, (1989), Wiley New York · Zbl 0676.34035 [4] Clark, C.W., Mathematical bio-economics: the optimal management of renewable resources, (1990), Wiley New York [5] Hirstova, S.G.; Bainov, D.D., Existence of periodic solutions of nonlinear systems of differential equations with impulsive effect, J. math. annl. appl., 125, 192-202, (1985) [6] Lakmeche, A.; Arino, O., Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment, Dynamics continuous, discrete impulsive systems, 7, 265-287, (2000) · Zbl 1011.34031 [7] Liu, X., Stability results for impulsive differential systems with application to population growth models, Dynamics stability systems, 9, 2, 163-174, (1994) · Zbl 0808.34056 [8] Sekhar, Ch.V.; Bhat, S.P.; Haddad, W.M., An invariance principle for nonlinear hybrid and impulsive dynamical systems, Nonlinear anal., 53, 527-550, (2003) · Zbl 1082.37018 [9] Tang, S.; Xiao, Y.; Chen, L.; Cheke, Bobert A., Integrated pest management models and their dynamical behaviour, Bull. math. biol., 67, 115-135, (2005) · Zbl 1334.91058 [10] Zhang, X.; Shuai, Zh.; Wang, K., Optimal impulsive harvesting policy for single population, Nonlinear anal.: real world appl., 4, 639-651, (2003) · Zbl 1011.92052 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.