We establish permanence conditions for a periodic predator–prey system with stage structure, pulse action, and Beddington–DeAngelis functional response.
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M. Fan and Y. Kuang, “Dynamics of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response,” J. Math. Anal. Appl., 295, 15–39 (2004).
T.W. Hwang, “Global analysis of the predator–prey system with Beddington–DeAngelis functional response,” J. Math. Anal. Appl., 281, 395–401 (2003).
W. G. Aiello and H. I. Freedman, “A time-delay model of single-species growth with stage structure,” Math. Biosci., 101, 139–153 (1990).
S. Ciu, L. Chen, and R. Agarwal, “Recent progress on stage-structured population dynamics,” Math. Comput. Modelling, 36, No. 11–13, 1319–1360 (2002).
J. Cui, L. Chen, and W. Wang, “The effect of dispersal on population growth with stage structure,” Comput. Math. Appl., 39, 91–102 (2000).
J. Cui and X. Song, “Permanence of predator–prey system with stage structure,” Discrete Contin. Dynam. Syst., Ser. B, 4, No. 3, 547–554 (2004).
J. Cui and Y. Takeuchi, “A predator–prey system with a stage structure for the prey,” Math. Comput. Modelling, 44, No. 11–12, 1126–1132 (2006).
K. Liu and L. Chen, “On a periodic time-dependent model of population dynamics with stage structure and impulsive effects,” Discrete Dynam. Nature Soc., ID 389727, 1–15 (2008).
W. Yang, X. Li, and Z. Bai, “Permanence of periodic Holling type-IV predator–prey system with stage structure for prey,” Math. Comput. Modelling, 48, No. 5–6, 677–684 (2008).
X. Liu and L. Chen, “Global dynamics of the periodic logistic system with periodic impulsive perturbations,” J. Math. Anal. Appl., 289, 279–291 (2004).
M. U. Akhmet, M. Beklioglu, T. Ergenc, and V. I. Tkachenko, “An impulsive ratio-dependent predator–prey system with diffusion,” Nonlin. Anal. Real World Appl., 7, No. 5, 1255–1267 (2006).
O. I. Kocherha, O. I. Nenya, and V. I. Tkachenko, “On positive periodic solutions of nonlinear impulsive functional differential equations,” Nonlin. Oscillations, 11, No. 4, 527–538 (2008).
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).
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Translated from Neliniini Kolyvannya, Vol. 12, No. 4, pp. 527–540, October–December, 2009.
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Myslo, Y.M., Tkachenko, V.I. On the permanence of periodic predator–prey systems with stage structure and pulse action. Nonlinear Oscill 12, 543–558 (2009). https://doi.org/10.1007/s11072-010-0093-1
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DOI: https://doi.org/10.1007/s11072-010-0093-1