| 一类恒化器模型正平衡解的稳定性 |
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| 引用本文： | 王欣雨,李艳玲.一类恒化器模型正平衡解的稳定性[J].纺织高校基础科学学报,2017,30(3). |
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| 作者姓名： | 王欣雨 李艳玲 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安,710119 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 在齐次Neumann条件下研究一类具有能量维持扩散的恒化器模型的稳定性.首先利用最大值原理和Harnack不等式给出平衡态方程正解的先验估计;其次利用谱分析和特征值理论证明正常数平衡解的一致渐近稳定性;最后借助构造Lyapunov函数来证明正常数平衡解的全局渐近稳定性.
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| 关 键 词： | 恒化器模型 Lyapunov凶数 全局渐近稳定性 |
Stability of positive equilibrium for a chemostat model |
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| WANG Xinyu,LI Yanling.Stability of positive equilibrium for a chemostat model[J].Basic Sciences Journal of Textile Universities,2017,30(3). |
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| Authors: | WANG Xinyu LI Yanling |
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| Abstract: | A diffusive chemostat model with maintenance energy is considered under homogeneous Neumann boundary condition.Firstly,by using the maximum principle and Harnack inequality,the estimates of the upper and positive lower bound of nonconstant positive steadystate solution is obtained.Secondly,the uniformly asymptotically stability of positive constant equilibrium is proved by using eigenvalue theory and the theory of spectral analysis.Finally,by constructing the Lyapunov function,the global asymptotic stability of the positive equilibrium is proved. |
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| Keywords: | chemostat model Lyapunov function global asymptotic stability |
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