The dynamics of an impulsive predator-prey system with stage structure and Holling type III functional response. (English) Zbl 1344.92138

Summary: Based on the biological resource management of natural resources, a stage-structured predator-prey model with Holling type III functional response, birth pulse, and impulsive harvesting at different moments is proposed in this paper. By applying comparison theorem and some analysis techniques, the global attractivity of predator-extinction periodic solution and the permanence of this system are studied. At last, examples and numerical simulations are given to verify the validity of the main results.


92D25 Population dynamics (general)
Full Text: DOI


[1] Li, W. X.; Wang, K., Optimal harvesting policy for general stochastic logistic population model, Journal of Mathematical Analysis and Applications, 368, 2, 420-428 (2010) · Zbl 1187.92081
[2] Das, T.; Mukherjee, R. N.; Chaudhuri, K. S., Harvesting of a prey-predator fishery in the presence of toxicity, Applied Mathematical Modelling, 33, 5, 2282-2292 (2009) · Zbl 1185.91120
[3] Zhang, R.; Sun, J. F.; Yang, H. X., Analysis of a prey-predator fishery model with prey reserve, Applied Mathematical Sciences, 1, 50, 2481-2492 (2007) · Zbl 1135.92331
[4] Zeng, Z. J., Asymptotically periodic solution and optimal harvesting policy for gompertz system, Nonlinear Analysis: Real World Applications, 12, 3, 1401-1409 (2011) · Zbl 1211.92046
[5] Song, X. Y.; Chen, L. S., Optimal harvesting and stability for a two-species competitive system with stage structure, Mathematical Biosciences, 170, 2, 173-186 (2001) · Zbl 1028.34049
[6] Kar, T. K., Selective harvesting in a prey-predator fishery with time delay, Mathematical and Computer Modelling, 38, 3-4, 449-458 (2003) · Zbl 1045.92046
[7] Jiang, X. W.; Song, Q.; Hao, M. Y., Dynamics behaviors of a delayed stage-structured predator-prey model with impulsive effect, Applied Mathematics and Computation, 215, 12, 4221-4229 (2010) · Zbl 1184.92054
[8] Jiao, J. J.; Meng, X. Z.; Chen, L. S., A stage-structured Holling mass defence predator-prey model with impulsive perturbations on predators, Applied Mathematics and Computation, 189, 2, 1448-1458 (2007) · Zbl 1117.92053
[9] Liu, Z. J.; Tan, R. H., Impulsive harvesting and stocking in a Monod-Haldane functional response predator-prey system, Chaos, Solitons and Fractals, 34, 2, 454-464 (2007) · Zbl 1127.92045
[10] Shao, Y.; Dai, B., The dynamics of an impulsive delay predator-prey model with stage structure and Beddington-type functional response, Nonlinear Analysis: Real World Applications, 11, 5, 3567-3576 (2010) · Zbl 1218.34099
[11] Song, X.; Hao, M.; Meng, X., A stage-structured predator-prey model with disturbing pulse and time delays, Applied Mathematical Modelling, 33, 1, 211-223 (2009) · Zbl 1167.34372
[12] Shao, Y. F.; Li, Y., Dynamical analysis of a stage structured predator-prey system with impulsive diffusion and generic functional response, Applied Mathematics and Computation, 220, 472-481 (2013) · Zbl 1329.92110
[13] Wei, F. Y.; Wang, K., Persistence of some stage structured ecosystems with finite and infinite delay, Nonlinear Analysis: Real World Application, 12, 1401-1409 (2011)
[14] Xiang, Z. Y.; Long, D.; Song, X. Y., A delayed Lotka-Volterra model with birth pulse and impulsive effect at different moment on the prey, Applied Mathematics and Computation, 219, 20, 10263-10270 (2013) · Zbl 1293.92021
[15] Jiao, J.; Cai, S.; Chen, L., Analysis of a stage-structured predatory-prey system with birth pulse and impulsive harvesting at different moments, Nonlinear Analysis. Real World Applications, 12, 4, 2232-2244 (2011) · Zbl 1220.34067
[16] Ma, Z.; Yang, J.; Jiang, G., Impulsive control in a stage structure population model with birth pulses, Applied Mathematics and Computation, 217, 7, 3453-3460 (2010) · Zbl 1202.92073
[17] Liu, J., Analysis of an epidemic model with density-dependent birth rate, birth pulses, Communications in Nonlinear Science and Numerical Simulation, 15, 11, 3568-3576 (2010) · Zbl 1222.37101
[18] Zhang, C.; Huang, N.-J.; O’Regan, D., Almost periodic solutions for a Volterra model with mutual interference and Holling type III functional response, Applied Mathematics and Computation, 225, 503-511 (2013) · Zbl 1334.34092
[19] Lv, Y. F.; Yuan, R.; Pei, Y. Z., A prey-predator model with harvesting for fishery resource with reserve area, Applied Mathematical Modelling, 37, 5, 3048-3062 (2013) · Zbl 1352.92128
[20] Shulgin, B.; Stone, L.; Agur, Z., Pulse vaccination strategy in the SIR epidemic model, Bulletin of Mathematical Biology, 60, 6, 1123-1148 (1998) · Zbl 0941.92026
[21] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), Singapore: World Scientific, Singapore · Zbl 0719.34002
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