Four positive periodic solutions of a discrete time Lotka-Volterra competitive system with harvesting terms

• Autorzy: Liu X. , Ren Y. , Li Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.

Słowa kluczowe

EN

discrete systems; Lotka-Volterra competitive models; coincidence degree; harvesting terms

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 2
• Strony: 257--267
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Liu X.

autor

Ren Y.

autor

Li Y.

• Yunnan Agricultural University Department of Applied Mathematics Kunming Yunnan 650221 People's Republic of China,

Bibliografia

• [1] Horst R. Thieme, Mathematics in Population Biology, [in:] Princeton Syries in Theoretial and Computational Biology, Princeton University Press, Princeton, NJ, 2003.
• [2] Z. Ma, Mathematical modelling and studing on species ecology, Education Press, Hefei, 1996 [in Chinese].
• [3] R.P. Agarwal, Difference Equations and Inequalities: Theory, Method and Applications, Monographs and Textbooks in Pure and Applied Mathematics, No. 228, Marcel Dekker, New York, 2000.
• [4] R.P. Agarwal, P.J.Y.Wong, Advance Topics in Difference Equations, Kluwer Publisher, Dordrecht, 1997.
• [5] H.I. Freedman, Deterministic Mathematics Models in Population Ecology, Marcel Dekker, New York, 1980.
• [6] J.D. Murray, Mathematical Biology, Springer-Verlag, New York, 1989.
• [7] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Boston, 1992.
• [8] M. Fan, K. Wang, Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system, Math. Comput. Modelling 35 (2002) 9–10, 951–961.
• [9] Y. Chen, Multiple periodic solutions of delayed predator-prey systems with type IV functional responses, Nonlinear Anal. Real World Appl. 5 (2004) 45–53.
• [10] Q. Wang, B. Dai, Y. Chen, Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response, Math. Comput. Modelling 49 (2009), 1829–1836.
• [11] D. Hu, Z. Zhang, Four positive periodic solutions to a Lotka-Volterra cooperative system with harvesting terms, Nonlinear Anal. Real World Appl. 11 (2010), 1115–1121.
• [12] Y. Li, Y. Kuang, Periodic solutions of periodic delay Lotka-Volterra equations and systems, J. Math. Anal. Appl. 255 (2001) 260–280.
• [13] Desheng Tian, Xianwu Zeng, Existence of at least two periodic solutions of a ratio-dependence predator-prey model with exploited term, Acta Math. Appl. Sin. English Ser. 21 (2005) 3, 489–494.
• [14] K. Zhao, Y. Ye, Four periodic solutions to a periodic Lotka-Volterra predatory-prey system with harvesting terms, Nonlinear. Anal. Real World Appl. (doi: 10.1016/j.nonrwa.2009.08.001).
• [15] R.Y. Zhang, et al., Periodic solutions of a single species discrete population modle with periodic harvest/stock, Comput. Math. Appl. 39 (2000) 77–90.
• [16] R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differetial Equitions, Springer Verlag, Berlin, 1977.