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具有饱和竞争项的捕食系统的二重分歧解及稳定性 被引量：1

Bifurcation solutions and stability of a predator-prey system with predator saturation and competition
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摘要 利用Lyapunov-Schmidt过程研究了一类具有饱和竞争项的捕食系统发自二重特征值处的分歧解的存在惟一性,并且判定了这些分歧解的渐近稳定性。 A predator-prey system with predator saturation and competition is investigated. The uniqueness, existence and stability of bifurcation solution which bifurcates from double multiplicity eigenvalue are obtained by using the Lyapunov-Schmidt procedure.
作者 冯孝周 聂华
机构地区 西安工业大学理学院 陕西师范大学数科院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2012年第5期103-107,114,共6页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金资助项目(10726042) 西安工业大学校长基金资助项目(XAGDXJJ1136) 陕西省教育厅科学基础研究计划项目(09JK480)
关键词 捕食系统 分歧解 渐近稳定性 predator-prey system bifurcation solutions asymptotical stability
分类号 O175.26 [理学—数学]
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参考文献17

  • 1LOTKA A J. Elements of physical biology[ M]. Baltimore: Williams and Wilkins, 1925. 被引量：1
  • 2DANCER E N. A counterexample of competing species equaions[J]. Diff Integ Eqns, 1996, 9:239-246. 被引量：1
  • 3DELGABO M, LoPEZ-GOMEZ J, SUAREZ A. On the dyboiotic Lotka-Volterra model with diffusion and transport effects[J]. J Diff Eqns, 2000, 160:175-262. 被引量：1
  • 4DU Yinhong, LOU Yuan. Qualotative behavior of positive solutions of a predator-prey model : effects of saturation [J].Proc R Soc Edinburgh Sect A, 2001, 131 (2) : 321-349. 被引量：1
  • 5DU Yihong, LOU Yuan. Some uniqueness and exact multiplicity results for a predator-prey model[ J]. Trans Amer Math Soc, 1997, 349:2443-2475. 被引量：1
  • 6WU Jianhua. Maximal attractor, stability and persistence for prey-predator model with saturation [ J]. Mathematical and Computer Modelling, 1999, 30:7-16. 被引量：1
  • 7CHEN Junping, ZHANG Hongde. The qualitative analysis of two species predator-prey model with Holling type III functional response[ J]. Appl Math Mech, 1986, 7( 1 ) :73-80. 被引量：1
  • 8HOLLING C S. The functional response of predators to prey density and its role in mimicry and populations [J]. Mem Entomol Soc Can, 1965, 45:3-60. 被引量：1
  • 9BAZYKIN A D. Nonlinear dynamics of interacting populations[M]. Singapore: World Scientific, 1998. 被引量：1
  • 10WANG Mingxin, WU Qiang. Positive solutions of a prey-predator model with predator saturation and competition [J]. J Math Anal Appl, 2008, 345:708-718. 被引量：1

二级参考文献12

  • 1Ye Q X,Li Z Y.Intoduction to Reaction-Diffusion Equations.Beijing:Scientific Press,1990. 被引量：1
  • 2Blat J,Brown K J.Global bifurcation of positive solutions in some systems of elliptic equtions.SIAM J.Math.Anal.,1986,17(6):1339-1353. 被引量：1
  • 3Kato T.Perturbation Theory of Linear Operators.New York:Springer-Verlag,1980. 被引量：1
  • 4Smoller J.Shock Waves and Reaction-Diffusion Equations.Springer-Verlag,New York,1982. 被引量：1
  • 5Crandall M G,Pabinowitz P H.Bifurcation,perturbation of simple eignvalues and linearized stability.Archive for Rational Mechanics Analysis,1973,52:161-180. 被引量：1
  • 6Crandall M G,Rabinowitz P H.Bifurcation from simple eigenvalues.J.Funct.Anal.,1971,8:321-340. 被引量：1
  • 7Rabinowitz P H.Some global results for nonlineat eigenvalue problems.J.Funct.Anal.,1971,7:487-513. 被引量：1
  • 8Bazykin A D.Nonlineat Dynamics of Interacting Populations.World Scientific,Singapore,1998. 被引量：1
  • 9Wang M X and Wu Q.Positive solutions of a prey-predator model with predator saturation and competition.J.Math.Anal.Appl.2008,345:708-718. 被引量：1
  • 10Wu J H.Maximal attractor,stability and persistence for prey-predator model with saturation.Mathematical and Computer Modelling,1999,30:7-16. 被引量：1

共引文献7

同被引文献13

  • 1SUN G Q,ZHANG G,JIN Z. Predator cannibalism can give rise to regular spatial pattern in a predator-prey system[J].{H}NONLINEAR DYNAMICS,2009,(1-2):75-84. 被引量：1
  • 2叶其孝;李正元;王明新.反应扩散方程引论[M]北京:科学出版社,2011. 被引量：1
  • 3DU Y H,LOU Y. Some uniqueness and exact multiplicity results for a predator-prey model[J].{H}Transactions of the American Mathematical Socity,1997,(06):2443-2475. 被引量：1
  • 4DANCER E N. On the indices of fixed points of mappings in cones and applications[J].{H}Journal of Mathematical Analysis and Applications,1983.131-151. 被引量：1
  • 5RUAN W H,FENG W. On the fixed point index and multiple steady-state solutions of reaction-diffusion systems[J].Differ-ential Integral Equations,1995,(02):371-392. 被引量：1
  • 6GUO G H,WU J H. Multiplicity and uniqueness of positive solutions for a predator-prey model with B-D functional response[J].Nonlinear Analysis:TMA,2010,(3-4):1632-1646. 被引量：1
  • 7DU Y H,LOU Y. S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model[J].{H}Journal of Differential Equations,1998,(02):390-440. 被引量：1
  • 8WANG M X,WU Q. Positive solutions of a prey-predator model with predator saturation and competition[J].{H}Journal of Mathematical Analysis and Applications,2008.708-718. 被引量：1
  • 9GUO G H,WU J H. The effect of mutual interference between predators on a predator-prey model with diffusion[J].{H}Journal of Mathematical Analysis and Applications,2012,(01):179-194. 被引量：1
  • 10GUO G H,WU J H. Multiplicity for a diffusive predator-prey mutualist model[J].{H}PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY,2012,(02):342-366. 被引量：1

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山东大学学报（理学版）
2012年 第5期

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