| 孟新柱,陈兰荪,张同迁.一类时滞捕食扩散系统全局分析[J].,2008,(3):456-464 |
| 一类时滞捕食扩散系统全局分析 |
| Global analysis for a predator-prey dispersal system with delays |
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| DOI：10.7511/dllgxb200803027 |
| 中文关键词: 连续时滞与无穷时滞 扩散 一致持久性 全局渐近稳定性 周期解 |
| 英文关键词: continuous and infinite time delays dispersion uniform permanence globally asymptotic stability periodic solution |
| 基金项目:国家自然科学基金资助项目(1047111710771179)；山东科技大学青年自然科学基金资助项目(05g016). |
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| 中文摘要: |
| 研究了一类非自治Lotka-Volterra型包含连续时滞与无穷时滞的捕食扩散系统． 首先，通过运用比较定理及时滞泛函微分方程基本理论，证明了该系统在一定条件下的一致持久性． 再者，通过构造适当的Lyapunov泛函， 获得了系统全局渐近稳定性的充分条件．最后由已知的文献推导出系统在持久性条件下具有至少一个正周期解．该模型及结果是对一些已知的模型及结论的改进与推广，目的是使之具有更丰富的生物意义． |
| 英文摘要: |
| A nonautonomous Lotka-Volterra predator-prey dispersal system with continuous and infinite time delays is considered. Firstly, by using comparison theorem and delay differential equation basic theory, the uniform permanence of the system under some appropriate conditions is proved. Secondly, by constructing suitable Lyapunov functional, the appropriate conditions for globally asymptotical stability of the system are obtained. Lastly, according to some results in the references, the system which has at least a positive periodic solution under the conditions for permanence is obtained. These results are basically an extension of the known results for nonautonomous Lotka-Volterra system, which enriches ecological meanings in models. |
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