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Multiple positive periodic solutions of n species delay competition systems with harvesting terms. (English) Zbl 1225.34094
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.
34K60Qualitative investigation and simulation of models
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
47N20Applications of operator theory to differential and integral equations
[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 · doi:10.1137/0523035
[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 · doi:10.1017/S0334270000004768
[4]Gopalsamy, K.: Stability and oscillations in delay differential equations of population dynamics, (1992) · 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 · doi:10.1017/S001708950000834X
[6]Kuang, Y.: Delay differential equations with applications in population dynamics, (1993) · 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 · doi:10.1090/S0002-9939-99-05210-7
[8]Gopalsamy, K.; Zhang, B. G.: On a neutral delay logistic equation, Dyn. stab. Syst. 2, 183-195 (1998) · Zbl 0665.34066 · doi:10.1080/02681118808806037
[9]Li, Y. K.: Periodic solutions for delay Lotka–Volterra competition systems, J. math. Anal. appl. 246, 230-244 (2000) · Zbl 0972.34057 · doi:10.1006/jmaa.2000.6784
[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 · doi:10.1006/jmaa.2000.7248
[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) · Zbl 0994.34059 · doi:10.1090/S0002-9939-01-06444-9
[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 · doi:10.1016/S0898-1221(02)00163-3
[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 · doi:10.1006/jmaa.2000.7181
[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 · doi:10.1080/00036818908839885
[16]Yang, P.; Xu, R.: Global attractivity of the periodic Lotka–Volterra system, J. math. Anal. appl. 233, 221-232 (1999) · Zbl 0973.92039 · doi:10.1006/jmaa.1999.6285
[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 · doi:10.1016/j.chaos.2006.09.025
[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 · doi:10.1016/S0025-5564(99)00022-X
[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 · doi:10.1016/j.jmaa.2006.08.063
[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 · doi:10.2748/tmj/1178225148
[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 · doi:10.1016/S0096-3003(03)00170-X
[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 · doi:10.1016/j.chaos.2005.08.028
[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 · doi:10.1016/j.chaos.2004.09.065
[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 · doi:10.1016/j.chaos.2004.01.007
[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 · doi:10.1016/j.chaos.2004.03.026
[27]Clark, C. W.: Mathematical bioeconomics: the optimal management of renewable resources, (1990) · Zbl 0712.90018
[28]Trowtman, L. J.: Variational calculus and optimal control, (1996)
[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 · doi:10.1007/BF01182789
[30]Gaines, R.; Mawhin, J.: Coincidence degree and nonlinear differetial equitions, (1977)
[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 · doi:10.1016/S1468-1218(03)00014-2
[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 · doi:10.1016/j.mcm.2008.09.008
[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 · doi:10.1016/j.nonrwa.2009.02.002
[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 · doi:10.1016/j.nonrwa.2006.08.009
[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 · doi:10.1016/j.nonrwa.2009.08.001