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Keywords:
multispecies predator-prey model; competition dynamic system; positive periodic solution; Beddington-DeAngelis functional; time delays response
multispecies predator-prey model; competition dynamic system; positive periodic solution; Beddington-DeAngelis functional; time delays response
Summary:
In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent).
References:
[1] Beddington, J. R.: Mutual interference between parasites or predators and its effect on searching efficiency. Journal of Animal Ecology 44 (1975), 331-340. DOI 10.2307/3866
[2] Beretta, E., Kuang, Y.: Convergence results in a well-known delayed predator-prey system. J. Math. Anal. Appl. 204 (1996), 840-853. DOI 10.1006/jmaa.1996.0471 | MR 1422776 | Zbl 0876.92021
[3] Bohner, M., Fan, M., Zhang, J.: Existence of periodic solutions in predator-prey and competition dynamic systems. Nonlinear Anal., Real World Appl. 7 (2006), 1193-1204. DOI 10.1016/j.nonrwa.2005.11.002 | MR 2260908 | Zbl 1104.92057
[4] Cai, Z., Huang, L., Chen, H.: Positive periodic solution for a multispecies competition-predator system with Holling III functional response and time delays. Appl. Math. Comput. 217 (2011), 4866-4878. DOI 10.1016/j.amc.2010.10.014 | MR 2763275 | Zbl 1206.92041
[5] DeAngelis, D. L., Goldstein, R. A., O'Neill, R. V.: A model for tropic interaction. Ecology 56 (1975), 881-892. DOI 10.2307/1936298
[6] Gaines, R. E., Mawhin, J. L.: Coincidence Degree, and Nonlinear Differential Equations. Lecture Notes in Mathematics 568 Springer, Berlin (1977). DOI 10.1007/BFb0089537 | MR 0637067 | Zbl 0339.47031
[7] Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Mathematics and its Applications 74 Kluwer Academic Publishers, Dordrecht (1992). MR 1163190 | Zbl 0752.34039
[8] Kuang, Y.: Delay Differential Equations: with Applications in Population Dynamics. Mathematics in Science and Engineering 191 Academic Press, Boston (1993). MR 1218880 | Zbl 0777.34002
[9] Li, Y.: Periodic solutions for delay Lotka-Volterra competition systems. J. Math. Anal. Appl. 246 (2000), 230-244. DOI 10.1006/jmaa.2000.6784 | MR 1761160 | Zbl 0972.34057
[10] Liu, G., Yan, J.: Positive periodic solutions of neutral predator-prey model with Beddington-DeAngelis functional response. Comput. Math. Appl. 61 (2011), 2317-2322. DOI 10.1016/j.camwa.2010.09.067 | MR 2785608 | Zbl 1219.34091
[11] Lu, S.: On the existence of positive periodic solutions to a Lotka-Volterra cooperative population model with multiple delays. Nonlinear Anal., Theory Methods Appl. 68 (2008), 1746-1753. DOI 10.1016/j.na.2007.01.003 | MR 2388847 | Zbl 1139.34317
[12] MacDonald, N.: Biological Delay Systems: Linear Stability Theory. Cambridge Studies in Mathematical Biology 9 Cambridge University Press, Cambridge (1989). MR 0996637 | Zbl 0669.92001
[13] Yang, S. J., Shi, B.: Periodic solution for a three-stage-structured predator-prey system with time delay. J. Math. Anal. Appl. 341 (2008), 287-294. DOI 10.1016/j.jmaa.2007.10.025 | MR 2394083 | Zbl 1144.34048
[14] Zeng, Z., Fan, M.: Study on a non-autonomous predator-prey system with Beddington-DeAngelis functional response. Math. Comput. Modelling 48 (2008), 1755-1764. DOI 10.1016/j.mcm.2008.05.052 | MR 2473405 | Zbl 1187.34052
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