Effects of pulse culling on population growth of migratory birds and economical birds. (English) Zbl 1242.92064

Summary: An increased number of economical birds is one of the major threats affecting migratory bird populations. We consider two competing species: rare migratory birds and economical birds, and investigate a nonautonomous two species competitive model with a Holling-type II functional response, in which pulse culling is incorporated. By utilizing an analytical method, sufficient and realistic conditions on permanence, extinction of the two species, existence of positive periodic solution, and global attractivity of semitrivial periodic solutions are established. The theoretical results are confirmed by numerical simulations.


92D40 Ecology
92D50 Animal behavior
34C60 Qualitative investigation and simulation of ordinary differential equation models
65C20 Probabilistic models, generic numerical methods in probability and statistics
Full Text: DOI


[1] Dong, L., Liao, J.: Neural network-based biomass estimation in the Poyang lake wetland using Envisat ASAR data. Remote Sens. Technol. Appl. 24, 325–330 (2009)
[2] http://en.wikipedia.org/wiki/Poyang_Lake (2010)
[3] Zhang, F., Gao, S.: On the migratory birds population model with pulse diffusion. In: Proceedings of the 7th Conference on Biological Dynamic System and Stability of Differential Equation, vol. 1, pp. 417–421. World Academic Press, Liverpool (2010)
[4] Chatterjee, S.: Role of migratory birds under environmental fluctuation–a mathematical study. J. Biol. Syst. 16, 81–106 (2008) · Zbl 1148.92030
[5] Wang, W., Shen, J.: Partial survival and extinction in two competing species with impulses. Nonlinear Anal., Real World Appl. 10, 1243–1254 (2009) · Zbl 1162.34308
[6] Hou, J., Teng, Z.: Permanence and global stability for nonautonomous N-species Lotka–Volterra competition system with impulses. Nonlinear Anal., Real World Appl. 11, 1882–1896 (2010) · Zbl 1200.34051
[7] Ahmad, S., Stamova, I.M.: Asymptotic stability of competitive systems with delays and impulsive perturbations. J. Math. Anal. Appl. 334, 686–700 (2007) · Zbl 1153.34044
[8] Teng, Z., Chen, L.: The positive periodic solutions in periodic Kolmogorov type systems with delays. Acta Math. Appl. Sin. 22, 446–456 (1999) (in Chinese) · Zbl 0976.34063
[9] Li, J., Yan, J.: Persistence for Lotka–Volterra patch-system with time delay. Nonlinear Anal., Real World Appl. 9, 490–499 (2008) · Zbl 1142.34048
[10] Nie, L., Teng, Z.: Qualitative analysis of a modified Leslie–Gower and Holling-type II predator-prey model with state dependent impulsive effects. Nonlinear Anal., Real World Appl. 11, 1364–1373 (2010) · Zbl 1228.37058
[11] Cui, J.: The effect of dispersal on permanence in a predator-prey population growth model. Comput. Math. Appl. 44, 1085–1097 (2002) · Zbl 1032.92032
[12] Liu, Z., Teng, Z.: Two patches impulsive diffusion periodic single-species logistic model. J. Biomath. 3, 127–141 (2010) · Zbl 1342.92188
[13] Teng, Z.: Uniform persistence of the periodic predator-prey Lotka–Volterra systems. Appl. Anal. 72, 339–352 (1998) · Zbl 1031.34045
[14] Cui, J.: Permanence of predator-prey system with periodic coefficients. Math. Comput. Model. 42, 87–98 (2005) · Zbl 1095.34019
[15] Tineo, A.: An iterative scheme for the N-competing species problem. J. Differ. Equ. 116, 1–15 (1995) · Zbl 0823.34048
[16] Ahmad, S., Montesde Oca, F.: Extinction in nonautonomous T-periodic competitive Lotka–Volterra system. Appl. Math. Comput. 90, 155–166 (1998) · Zbl 0906.92024
[17] Ahmad, S., Montesde Oca, F.: Average growth and extinction in a two dimensional Lotka–Volterra system. Dyn. Contin. Discrete Impuls. Syst. 9, 177–186 (2002) · Zbl 1081.34513
[18] Montesde Oca, F., Zeeman, M.L.: Extinction in nonautonomous competitive Lotka–Volterra systems. Proc. Am. Math. Soc. 124, 3677–3687 (1996) · Zbl 0866.34029
[19] Teng, Z., Li, Z.: Permanence and asymptotic behavior of the N-species nonautonomous Lotka–Volterra competitive systems. Comput. Math. Appl. 39, 107–116 (2000) · Zbl 0959.34039
[20] Cui, J., Chen, L.: The effect of dispersal on population growth with stage-structure. Comput. Math. Appl. 39, 91–102 (2000) · Zbl 0968.92018
[21] Cui, J., Chen, L.: The effect of habitat fragmentation and ecological invasion on population sizes. Comput. Math. Appl. 38, 1–11 (1999) · Zbl 0939.92033
[22] Bainov, D.D., Simeonov, P.S.: Impulsive Differential Equations: Periodic Solutions and Applications. Longman, London (1993) · Zbl 0815.34001
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.