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E. Beretta and Y. Takeuchi, “Global Stability of SingleSpecies Diffusion Volterra Models with Continuous Time Delays,” Bulletin of Mathematical Biology, Vol. 49, 1987, pp. 431-448.

has been cited by the following article:

• TITLE: A Single Species Model with Symmetric Bidirectional Impulsive Diffusion and Dispersal Delay

  AUTHORS: Haiyun Wan, Long Zhang, Hongli Li

  KEYWORDS: Dispersal Delay; Impulsive Diffusion; Permanence; Global Stability; Periodic Solution

  JOURNAL NAME: Applied Mathematics, Vol.3 No.9, September 27, 2012

  ABSTRACT: In the natural ecosystem, impulsive diffusion provides a more natural description for population dynamics. In addition, dispersal processes often involve with time delay. In view of these facts, a single species model with impulsive diffusion and dispersal delay is formulated. By the stroboscopic map of the discrete dynamical system and other analysis methods, the permanence of the system is investigated. Moreover, sufficient conditions on the existence and uniqueness of a positive periodic solution for the system are derived from the intermediate value theorem. We also demonstrate the global stability of the positive periodic solution by the theory of discrete dynamical system. Finally, numerical simulations and discussion are presented to validate our theoretical results.