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

• 作者: Haiyun Wan Hongli Li Long Zhang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Dispersal DELAY IMPULSIVE Diffusion PERMANENCE Global Stability PERIODIC Solution
• 年，卷（期）: 2012,（9）
• 页码范围: 1079-1088
• 页数: 10页
• 分类号: O1

摘要

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.