| 王晓梅,钟守铭.带有脉冲控制的生物系统种群持久存在性问题研究[J].数学研究及应用,2011,31(6):1035~1046 |
| 带有脉冲控制的生物系统种群持久存在性问题研究 |
| Species Permanence Analysis of an Ecological Model with an Impulsive Control Strategy |
| 投稿时间：2010-07-08 修订日期：2011-01-12 |
| DOI：10.3770/j.issn:1000-341X.2011.06.011 |
| 中文关键词: 脉冲控制策略 局部渐近稳定 周期解 持久生存. |
| 英文关键词:impulsive control strategy locally asymptotically stable complex dynamics periodic solution. |
| 基金项目:国家自然科学基金(Grant No.Y60804015),国家重点基础研究规划资助项目 (Grant No.Y2010CB732501). |
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| 中文摘要: |
| 在本论文中,依据生物学意义和微分方程理论,一个带有脉冲效应的生物系统被建立.通过利用脉冲微分方程理论和比较定理,首先证明了系统的周期解是全局渐近稳定的;其次得到保持系统持久生存的关键条件.此外,数值模拟进一步验证了理论结果的正确性和在一定参数取值下,系统是有可能持久生存的.最后希望所有的研究结果对今后生物系统的动力学行为研究有一定的作用. |
| 英文摘要: |
| In this paper, on the basis of the theories and methods of ecology and ordinary differential equations, an ecological model with an impulsive control strategy is established. By using the theories of impulsive equations, small amplitude perturbation skills and comparison technique, we get the condition which guarantees the global asymptotical stability of the prey-$x$-eradication and predator-$y$-eradication periodic solution. It is proved that the system is permanent. Furthermore, numerical simulations are also illustrated which agree well with our theoretical analysis. All these results may be useful in study of the dynamic complexity of ecosystems. |
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