Convergence Results in a Well-Known Delayed Predator-Prey System

  title={Convergence Results in a Well-Known Delayed Predator-Prey System},
  author={Edoardo Beretta and Yang Kuang},
  journal={Journal of Mathematical Analysis and Applications},
  • E. Beretta, Y. Kuang
  • Published 15 December 1996
  • Mathematics
  • Journal of Mathematical Analysis and Applications
Abstract In this paper, we provide a 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 with a single discrete delay. Our procedure requires the delay length to be small. A detailed example is presented. The method used here is to construct a proper Liapunov functional in a restricted region. 
Dynamics of a delayed Lotka-Volterra model with two predators competing for one prey
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  • Environmental Science
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  • 1973
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