In this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results.

中文翻译：

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具有反馈控制的半离散物流系统的全局稳定性

本文提出了一种具有狄利克雷边界条件和反馈控制的半离散逻辑模型。借助子解和超解法以及特征值理论，证明了唯一的正平衡。通过构建合适的Lyapunov函数，研究了唯一正平衡的全局无症状稳定性。最后，通过数值模拟验证了主要结果的有效性。