Li, Yongkun; Zhao, Kaihong; Ye, Yuan Multiple positive periodic solutions of \(n\) species delay competition systems with harvesting terms. (English) Zbl 1225.34094 Nonlinear Anal., Real World Appl. 12, No. 2, 1013-1022 (2011). The authors explore the periodicity of a delay periodic Lotka-Volterra type multi-species competitive system with harvesting terms and derive sufficient conditions for the existence of multiple positive periodic solutions by using a continuation theorem from coincidence degree theory. Reviewer: Meng Fan (Changchun) Cited in 18 Documents MSC: 34K60 Qualitative investigation and simulation of models involving functional-differential equations 34K13 Periodic solutions to functional-differential equations 92D25 Population dynamics (general) 47N20 Applications of operator theory to differential and integral equations Keywords:periodic solutions; delay competition system; coincidence degree PDFBibTeX XMLCite \textit{Y. Li} et al., Nonlinear Anal., Real World Appl. 12, No. 2, 1013--1022 (2011; Zbl 1225.34094) Full Text: DOI References: [1] Freedman, H. I.; Kuang, Y., Stability switches in linear scalar neutral delay equations, Funkcial. Ekvac., 34, 187-209 (1991) · Zbl 0749.34045 [2] Freedman, H. I.; Wu, J., Periodic solutions of single-species models with periodic delay, SIAM J. Math. Anal., 23, 689-701 (1992) · Zbl 0764.92016 [3] Gopalsamy, K., Global asymptotic stability in a periodic Lotka-Volterra system, J. Aust. Math. Soc. Ser. B, 27, 66-72 (1985) · Zbl 0588.92019 [4] Gopalsamy, K., Stability and Oscillations in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Boston · Zbl 0752.34039 [5] Gopalsamy, K.; He, X.; Wen, L., On a periodic neutral logistic equation, Glasg. Math. J., 33, 281-286 (1991) · Zbl 0737.34050 [6] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press: Academic Press New York · Zbl 0777.34002 [7] Li, Y. K., Periodic solutions of a periodic delay predator-prey system, Proc. Amer. Math. Soc., 127, 1331-1335 (1999) · Zbl 0917.34057 [8] Gopalsamy, K.; Zhang, B. G., On a neutral delay logistic equation, Dyn. Stab. Syst., 2, 183-195 (1998) · Zbl 0665.34066 [9] Li, Y. K., Periodic solutions for delay Lotka-Volterra competition systems, J. Math. Anal. Appl., 246, 230-244 (2000) · Zbl 0972.34057 [10] Li, Y. K.; Kuang, Y., Periodic solutions of periodic delay Lotka-Volterra equations and systems, J. Math. Anal. Appl., 255, 260-280 (2001) · Zbl 1024.34062 [11] Li, Y. K.; Kuang, Y., Periodic solutions in periodic delayed Gause-type predator-prey systems, Proc. Dynam. Syst. Appl., 3, 375-382 (2001) · Zbl 1009.34063 [12] Li, Y. K.; Y, Kuang, Periodic solutions in periodic state-dependent delay equations and population models, Proc. Amer. Math. Soc., 130, 135-153 (2002) [13] Jin, Z.; Zhien, M., Periodic solutions for delay differential equations model of plankton allelopathy, Comput. Math. Appl., 44, 491-500 (2002) · Zbl 1094.34542 [14] Fan, M.; Wang, K., Global existence of positive periodic solutions of periodic predator-prey system with infinite delay, J. Math. Anal. Appl., 262, 1-11 (2001) · Zbl 0995.34063 [15] Ma, Z. E.; Wang, W. D., Asymptotic behavior of predator-prey system with time dependent coefficients, Appl. Anal., 34, 79-90 (1989) · Zbl 0658.34044 [16] Yang, P.; Xu, R., Global attractivity of the periodic Lotka-Volterra system, J. Math. Anal. Appl., 233, 221-232 (1999) · Zbl 0973.92039 [17] Li, Y. K., Positive periodic solutions of periodic neutral Lotka-Volterra system with distributed delays, Chaos Solitons Fractals, 37, 288-298 (2008) · Zbl 1145.34361 [18] Fan, M.; Wang, K.; Jiang, D., Existence and global attractivity of positive periodic solutions of periodic \(n\)-species Lotka-Volterra competition systems with several deviating arguments, Math. Biosci., 160, 47-61 (1999) · Zbl 0964.34059 [19] Li, Y. K., Positive periodic solutions of periodic neutral Lotka-Volterra system with state dependent delays, J. Math. Anal. Appl., 330, 1347-1362 (2007) · Zbl 1118.34059 [20] Tang, B.; Kuang, Y., Existence, uniqueness and as asymptotic stability of periodic solutions of periodic functional differential systems, Tohoku Math. J., 49, 217-239 (1997) · Zbl 0883.34074 [21] Li, Y. K.; Zhu, L. F., Existence of periodic solutions of discrete Lotka-Volterra systems with delays, Bull. Inst. Math. Acad. Sin., 33, 369-380 (2005) · Zbl 1087.39013 [22] Yang, Z.; Cao, J., Positive periodic solutions of neutral Lotka-Voltrra system with periodic delays, Appl. Math. Comput., 149, 661-687 (2004) · Zbl 1045.92037 [23] Zhao, H.; Ding, N., Existence and global attractivity of positive periodic solution for competition-predator system with variable delays, Chaos Solitons Fractals, 29, 162-170 (2006) · Zbl 1106.37052 [24] Zhen, J.; Han, M.; Li, G., The persistence in a Lotka-Volterra competition systems with impulsive, Chaos Solitons Fractals, 24, 1105-1117 (2005) · Zbl 1081.34045 [25] Zhen, J.; Ma, Z.; Han, M., The existence of periodic solutions of the \(n\)-species Lotka-Volterra competition systems with impulsive, Chaos Solitons Fractals, 22, 181-188 (2004) · Zbl 1058.92046 [26] Song, Y.; Han, M.; Peng, Y., Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays, Chaos Solitons Fractals, 22, 1139-1148 (2004) · Zbl 1067.34075 [27] Clark, C. W., Mathematical Bioeconomics: The Optimal Management of Renewable Resources (1990), Wiley: Wiley New York · Zbl 0712.90018 [28] Trowtman, L. J., Variational Calculus and Optimal Control (1996), Springer: Springer New York [29] Leung, A. W., Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka system, Appl. Math. Optim., 31, 219-241 (1995) · Zbl 0820.49011 [30] Gaines, R.; Mawhin, J., Coincidence Degree and Nonlinear Differetial Equitions (1977), Springer Verlag: Springer Verlag Berlin [31] Chen, Y., Multiple periodic solutions of delayed predator-prey systems with type IV functional responses, Nonlinear Anal. RWA, 5, 45-53 (2004) · Zbl 1066.92050 [32] Wang, Q.; Dai, B.; Chen, Y., Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response, Math. Comput. Modelling, 49, 1829-1836 (2009) · Zbl 1171.34341 [33] Hu, D.; Zhang, Z., Four positive periodic solutions to a Lotka-Volterra cooperative system with harvesting terms, Nonlinear Anal. RWA, 11, 1115-1121 (2010) · Zbl 1187.34050 [34] Zhang, Z.; Tian, Tesheng, Multiple positive periodic solutions for a generalized predator-prey system with exploited terms, Nonlinear Anal. RWA, 9, 26-39 (2008) · Zbl 1145.34051 [35] Zhao, K.; Ye, Y., Four positive periodic solutions to a periodic Lotka-Volterra predatory-prey system with harvesting terms, Nonlinear Anal. RWA, 11, 2448-2455 (2010) · Zbl 1201.34074 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.