In this paper, we consider a hybrid network model of delayed predator-prey Gompertz systems with impulsive diffusion between two patches, in which the patches represent nodes of the network such that the prey population interacts locally in each patch and diffusion occurs along the edges connecting the nodes. Using the discrete dynamical system determined by the stroboscopic map which has a globally stable positive fixed point, we obtain the global attractive condition of predator-extinction periodic solution for the network system. Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network.

中文翻译：

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时滞捕食-被捕食Gompertz系统的混杂网络模型的动力学分析。

在本文中，我们考虑了具有两个斑块之间脉冲扩散的时滞捕食者－猎物Gompertz系统的混合网络模型，其中，这些斑块表示网络的节点，使得猎物种群在每个斑块中局部相互作用，并且沿着连接的边沿发生扩散节点。利用由频闪观测图确定的具有全局稳定的正不动点的离散动力系统，我们得到了网络系统捕食-灭绝周期解的全局吸引条件。此外，通过使用时滞泛函和脉冲微分方程理论，我们获得了具有时延的充分条件，以保证网络的持久性。