대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제43권3호
  • /
  • Pages.575-587
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  • 2006
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE ASYMPTOTIC STABILITY BEHAVIOR IN A LOTKA-VOLTERRA TYPE PREDATOR-PREY SYSTEM

  • Ko, Youn-Hee (Department of Mathematics Education, Cheju National University)
  • 발행 : 2006.08.01
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초록

In this paper, we provide 3 detailed and explicit procedure of obtaining some regions of attraction for the positive steady state (assumed to exist) of a well known Lotka-Volterra type predator-prey system. Also we obtain the sufficient conditions to ensure that the positive equilibrium point of a well known Lotka-Volterra type predator-prey system with a single discrete delay is globally asymptotically stable.

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참고문헌

  1. Y. Cao and H. I. Freedman, Global attractivity in time-delayed predator-prey system. J. Austral. Math. Soc. Ser. B 38 (1996), no. 2, 149-162 https://doi.org/10.1017/S0334270000000540
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  3. J. K. Hale, Ordinary Differential Equations, Wiley-Interscience, New York, 1977
  4. X. Z. He, Stability and Delays in a Predator-Prey System, J. Math. Anal. Appl. 198 (1996), no. 2, 355-370 https://doi.org/10.1006/jmaa.1996.0087
  5. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993
  6. D. Mukherjee and A. B. Roy, Uniform persistence and global attractivity theorem for generalized prey-predator system with time delay, Nonlinear Anal. 38 (1999), no. 1, Ser. B : Real World Appl., 59-74 https://doi.org/10.1016/S0362-546X(99)00096-6
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피인용 문헌

  1. Analysis of a stage-structured predator-prey model with Crowley-Martin function vol.36, pp.1-2, 2011, https://doi.org/10.1007/s12190-010-0413-8