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Global attractivity of a stage-structure variable coefficients predator-prey system with time delay and impulsive perturbations on predators. (English) Zbl 1155.92355

Summary: We consider a delayed stage-structured variable coefficients predator-prey system with impulsive perturbations on predators. By using the discrete dynamical system determined by the stroboscopic map and the standard comparison theorem, we obtain sufficient conditions which guarantee the global attractivity of prey-extinction periodic solutions of the investigated system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide a reliable tactic basis for practical pest management.

MSC:

92D40 Ecology
34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
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[1] DOI: 10.1142/0906 · doi:10.1142/0906
[2] Bainov D., Impulsive Differential Equations: Periodic Solutions and Applications (1993) · Zbl 0815.34001
[3] DOI: 10.2307/2403471 · doi:10.2307/2403471
[4] Paneyya J. C., Bull. Math. Biol. 58 pp 425–
[5] DOI: 10.1016/S0096-3003(01)00156-4 · Zbl 1024.92017 · doi:10.1016/S0096-3003(01)00156-4
[6] Xiao Y. N., Acta Math. Appl. English Series 16 pp 607–
[7] DOI: 10.1016/S1468-1218(01)00021-9 · Zbl 1007.92032 · doi:10.1016/S1468-1218(01)00021-9
[8] Xiao Y. N., J. Syst. Sci. Compl. 16 pp 275–
[9] Lu Z. H., Acta Math. Sci. 4 pp 440–
[10] DOI: 10.1137/S0036144500371907 · Zbl 0993.92033 · doi:10.1137/S0036144500371907
[11] Zaghrout A. A. S., Appl. Math. Comput. 77
[12] Aiello W. G., SIAM J. Appl. Math. 52
[13] DOI: 10.1007/978-3-662-08539-4 · doi:10.1007/978-3-662-08539-4
[14] DOI: 10.1016/0025-5564(90)90019-U · Zbl 0719.92017 · doi:10.1016/0025-5564(90)90019-U
[15] DOI: 10.1016/0022-247X(90)90289-R · Zbl 0711.34091 · doi:10.1016/0022-247X(90)90289-R
[16] DOI: 10.1007/BF02462319 · Zbl 0606.92020 · doi:10.1007/BF02462319
[17] DOI: 10.1007/BF02459701 · Zbl 0614.92015 · doi:10.1007/BF02459701
[18] DOI: 10.1073/pnas.42.9.699 · Zbl 0072.37005 · doi:10.1073/pnas.42.9.699
[19] Fisher M. E., J. Math. Biol. 19 pp 117–
[20] K. Yang, Delay Differential Equation with Application in Population Dynamics (Academic Press, New York, 1987) pp. 67–70.
[21] DOI: 10.1007/BF02460938 · Zbl 0451.92011 · doi:10.1007/BF02460938
[22] DOI: 10.1016/S0893-9659(01)00153-7 · Zbl 1015.92033 · doi:10.1016/S0893-9659(01)00153-7
[23] DeBach P., Biological Control of Insect Pests and Weeds (1964)
[24] DeBach P., Biological Control by Natural Enemies (1991)
[25] DOI: 10.1016/0025-5564(76)90080-8 · Zbl 0373.92023 · doi:10.1016/0025-5564(76)90080-8
[26] DOI: 10.1016/S0025-5564(00)00051-1 · Zbl 0966.92026 · doi:10.1016/S0025-5564(00)00051-1
[27] DOI: 10.1146/annurev.en.34.010189.000245 · doi:10.1146/annurev.en.34.010189.000245
[28] DOI: 10.1016/S0960-0779(02)00408-3 · Zbl 1085.34529 · doi:10.1016/S0960-0779(02)00408-3
[29] K. Yang, Delay Differential Equation with Application in Population Dynamics (Academic Press, New York, 1987) pp. 67–70.
[30] DOI: 10.1007/BF02460938 · Zbl 0451.92011 · doi:10.1007/BF02460938
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