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The effect of impulsive diffusion on dynamics of a stage-structured predator-prey system. (English) Zbl 1201.92060
Summary: We investigate a predator-prey model with impulsive diffusion of the predator and stage structure of prey. A globally attractive condition of prey-extinction periodic solutions of the system is obtained by the stroboscopic map of the discrete dynamical system. The permanence condition of the system is also obtained by the theory of impulsive delay differential equations. The results indicate that the discrete time delay has influence on the dynamical behavior of the system. Finally, some numerical simulations are carried out to support the analytic results.

MSC:
92D40 Ecology
37N25 Dynamical systems in biology
65C60 Computational problems in statistics (MSC2010)
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References:
[1] DOI: 10.1007/978-3-540-74331-6_5
[2] Theoretical Population Biology 65 pp 299– (2004) · Zbl 1109.92047
[3] DOI: 10.1016/S0092-8240(83)80052-4
[4] DOI: 10.1006/jmaa.2000.7385 · Zbl 0985.34061
[5] American Naturalist 108 pp 207– (1994)
[6] Journal of Systems Science and Complexity 15 (3) pp 307– (2002)
[7] DOI: 10.1016/0025-5564(90)90019-U · Zbl 0719.92017
[8] DOI: 10.1137/0148035 · Zbl 0661.92018
[9] DOI: 10.1016/S0092-8240(87)80005-8
[10] DOI: 10.1016/0270-0255(87)90689-0
[11] DOI: 10.1016/0022-247X(86)90029-6 · Zbl 0588.92020
[12] DOI: 10.1016/0362-546X(89)90026-6 · Zbl 0685.92018
[13] DOI: 10.1080/00036818908839829 · Zbl 0641.92016
[14] Pitman Monographs and Surveys in Pure and Applied Mathematics 66 pp x+228– (1993)
[15] DOI: 10.1006/tpbi.1993.1026 · Zbl 0782.92020
[16] DOI: 10.1007/s10255-005-0213-3 · Zbl 1180.92072
[17] DOI: 10.1216/rmjm/1181072290 · Zbl 0832.34039
[18] Dynamics of Continuous, Discrete and Impulsive Systems 7 (2) pp 265– (2000)
[19] DOI: 10.1016/S0960-0779(02)00408-3 · Zbl 1085.34529
[20] DOI: 10.1093/imamci/15.3.269 · Zbl 0949.93069
[21] DOI: 10.1016/S0898-1221(98)00178-3 · Zbl 0962.35181
[22] DOI: 10.1016/S0092-8240(98)90005-2 · Zbl 0941.92026
[23] DOI: 10.1016/S0960-0779(00)00111-9 · Zbl 0976.92033
[24] DOI: 10.1016/j.chaos.2006.01.102 · Zbl 1131.92071
[25] DOI: 10.1016/0025-5564(87)90051-4 · Zbl 0634.92017
[26] DOI: 10.1142/S1793524508000151 · Zbl 1155.92356
[27] DOI: 10.1142/S1793524508000163 · Zbl 1155.92355
[28] DOI: 10.1016/j.amc.2007.04.098 · Zbl 1126.92052
[29] Biomathematics 19 pp xiv+767– (1989)
[30] DOI: 10.1016/S0898-1221(97)00056-4
[31] DOI: 10.1016/j.amc.2006.12.043 · Zbl 1117.92053
[32] DOI: 10.1016/j.chaos.2007.01.003 · Zbl 1146.34322
[33] DOI: 10.1016/j.chaos.2007.11.015 · Zbl 1198.34153
[34] DOI: 10.1016/j.chaos.2006.07.003 · Zbl 1128.92054
[35] DOI: 10.1016/j.chaos.2006.01.102 · Zbl 1131.92071
[36] Series in Modern Applied Mathematics 6 pp xii+273– (1989)
[37] DOI: 10.1016/S0252-9602(07)60040-X · Zbl 1125.92052
[38] (1987)
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