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具有时滞反应扩散方程组的全局渐近稳定性 被引量：1

Global Asymptotic Stability of Reaction-Diffusion Systems with Time Delays
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摘要 研究了具有时滞反应扩散方程组的初边值问题,采用比较原理、解的存在性定理,得到了解的存在性和平衡态方程正解的全局渐近稳定性的充分条件.这个结果导致捕食食饵系统的持久性、平凡解和所有半平凡解的不稳定性和不存在非一致平衡解. Adopting the comparison principle and the theory of existence, the initial and boundary conditions of reaction-diffusion systems with time delays are dealt with to obtain the sufficient conditions for the existence of solutions and global asymptotic stability of a positive steady-state solution. The result leads to the permanence of the prey-predator systems, the instability of the trivial and all forms of semitrivial solutions, and the nonexistence of nonuniform steady-state solutions.
作者 李艳玲 马逸尘
机构地区 西安交通大学理学院
出处 《西安交通大学学报》 EI CAS CSCD 北大核心 2005年第4期437-440,共4页 Journal of Xi'an Jiaotong University
基金 国家自然科学基金资助项目(10371096) 教育部优秀青年教师资助计划项目.
关键词 反应扩散方程 时滞 全局渐近稳定性 捕食-食饵模型 比较原理 Boundary conditions Delay control systems Matrix algebra Numerical methods State estimation
分类号 O175.29 [理学—基础数学]
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参考文献11

  • 1Du Y H, Lou Y. S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model [J]. J Differential Equations, 1998,144(2):390-440.
  • 2Leung A, Clark D C. Bifurcations and large-time asymptotic behavior for prey-predator reaction-diffusions with Dirichlet boundary data [J]. J Differential Equations, 1980,35(1):113-127.
  • 3Ruan W H, Feng W. On the fixed point index and multiple steady-state solutions of reaction diffusion systems [J]. Differential Integral Equations, 1995,8(2):371-392.
  • 4Lu Z Y, Takeuchi Y. Permanence and global attractivity for competitive Lotka-Volterra systems with delay [J].Nonlinear Analysis, 1994,22(7):847-856.
  • 5Brown K J, Hess P. Positive periodic solutions of predator-prey reaction-diffusion systems [J]. Nonlinear Analysis, 1991,16(10): 1 147-1 158.
  • 6Ruan S G, Zhao X Q.Persistence and extinction in two species reaction diffusion systems with delays [J].J Differential Equations, 1999,156(1):71-92.
  • 7谢强军,吴建华,黑力军.一类反应扩散方程非负平衡解的存在性[J].数学学报（中文版）,2004,47(3):467-478. 被引量：10
  • 8Du Y. Positive periodic solutions of a competitor-competitor-mutualist model[J].Differential Integral equations, 1996,19(4):1 043-1 066.
  • 9Pao C V. Convergence of solutions of reaction-diffusion systems with time delays [J].Nonlinear Analysis,2002,48(3):349-362.
  • 10Feng W. Coexistence, stability, and limiting behavior in a one-predator-two-prey model [J]. J Math Anal Appl, 1993,179(2):592-609.

二级参考文献19

  • 1Pao C. V., Nolinear parabolic and elliptic equations, New York: Plenum Press, 1992.
  • 2Blat J., Brown K. J., Bifurcation of steady-state solutions in predator-prey and competition systems, Proc.Roy. Soc. Edinburgh, 1984, 97A: 21-34.
  • 3Dancer E. N., Lopez-Gomez J., Ortega R., On the spectrum of some linear noncooperative elliptic systems with radial symmetry, Differential and Integral Equations, 1995, 8(3): 515-523.
  • 4Li L., Coexistence theorems of steady state for predator-prey interact systems, Trans. Amer. Math. Soc.,1988, 305: 143-166.
  • 5Wang M. X., Nonlinear parabolic equations, Beijing: Scientific Press, 1993 (in Chinese).
  • 6Brown K. J., Hess P., Positive periodic solutions of predator-prey reaction-diffusion systems, Nonlinear Anal.,1991, 16(12): 1147-1158.
  • 7Brown K. J., Nontrivial solutions of predator-prey systems with small diffusion, Nonlinear Anal., 1987, 11:685-689.
  • 8Conway E. D., Gardner R., Smoller J., Stability and bifurcation of steady state solutions for predator-prey equations, Adv. Appl. Math., 1982, 3: 288-334.
  • 9Blat J., Brown K.J., Global bifurcation of positive solutions in some systems of elliptic equations, SIAM J.Math. Anal., 1986, 17: 1339-1353.
  • 10Du Y., Lou Y., Some uniqueness and exact multiplicity results for a predator-preymodel, Trans. Amer.Math. Soc., 1997, 349(6): 2443-2475.

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西安交通大学学报
2005年 第4期

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