数学与计算机科学 |
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一类带有比率依赖型反应函数的捕食-食饵模型正解的存在性和多重性 |
李海侠 |
宝鸡文理学院数学与信息科学学院, 陕西宝鸡 721013 |
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The existence and multiplicity of positive solutions for a predator-prey model with ratio-dependent type functional response |
LI Haixia |
Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi Province, China |
[1] BLAT J, BROWN K J. Global bifurcation of positive solutions in some systems of elliptic equations[J]. SIAM J Math Anal,1986,17(6):1339-1353. [2] DU Y H, LOU Y. Some uniqueness and exact multiplicity results for a predator-prey models[J]. Transactions of the American Mathematical Society,1997,349(6):2443-2475. [3] WANG M X, WU Q. Positive solutions of a prey-predator model with predator saturation and competition[J]. J Math Anal Appl,2008,345(2):708-718. [4] WEI M H, WU J H, GUO G H. The effect of predator competition on positive solutions for a predator-prey model with diffusion[J]. Nonlinear Analysis,2012,75(13):5053-5068. [5] RYU N, AHN I. Positive solutions for ratio-dependent predator-prey interaction systems[J]. J Differential Equations,2005,218(1):117-135. [6] SHI X Y, ZHOU X Y, SONG X Y. Analysis of a stage-structured predator-prey model with Crowley-Martin function[J]. J Appl Math Comput,2011,36(1):459-472. [7] LIU X, LIU Y W. Dynamic behavior of a delayed modified Leslie predator prey system with Crowley-Martin functional response and feedback controls[J]. Advances in Mathematics,2012,41(4):501-511. [8] DON Q L, MA W B, SUN M J. The asymptotic behavior of a chemostat model with Crowley-Martin type functional response and tim delays[J]. J Math Chem,2013,51(5):1231-1248. [9] LI H X. Asymptotic behavior and multiplicity for a diffusive Leslie-Gower predator-prey system with Crowley-Martin functional response[J]. Computers and Mathematics with Applications,2014,68(7):693-705. [10] 李海侠,李艳玲.一类带有Crowley-Martin反应函数的捕食-食饵模型的定性分析[J].中山大学学报:自然科学版,2014,53(5):66-72. LI Haixia, LI Yanling. Qualitative analysis for a predator-prey system with Crowley-Martin type functional response[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(5):66-72. [11] CRANDALL M G, RABINOWITZ P H. Bifurcation from simple eigenvalue[J]. J Funct Anal,1971,8(2):321-340. [12] LI L. Coexistence theorems of steady-states for predator-prey interacting systems[J]. Trans Amer Math Soc,1988,305(1):143-166. [13] WU J H. Global bifurcation of coexistence state for the competition model in the chemostat[J]. Nonlinear Analysis,2000,39(39):817-835. [14] RABINOWITZ P H. Some global results for nonlinear eigenvalue problems[J]. J Funct Anal,1971,7(3):487-513. [15] KUANG Y, BERETTA E. Global qualitative analysis of a ratio-dependent predator-prey system[J]. J Math Biol,1998,36(4):389-406. [16] BAEK S, KO W, AHN I. Coexistence of a one-prey two-predators model with ratio-dependent functional responses[J]. Applied Mathematics and Computation,2012,219(4):1897-1908. [17] DANCER E N. On the indices of fixed points of mapping in cones and applications[J]. J Math Anal Appl,1983,91(1):131-151. |
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