Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050, Gansu, People's Republic of China.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People's Republic of China.
J Math Biol. 2024 Sep 28;89(4):44. doi: 10.1007/s00285-024-02140-6.
Based on the patchy habitats of mistletoes and the mutualistic relationship between mistletoes and birds, we propose a mistletoe-bird model on a weighted network that is described by discrete Laplacian operators. Without considering mistletoes, the dynamics of a model of birds is investigated by a threshold parameter. Under the premise of the persistence of birds, the existence and uniqueness of solutions of a mistletoe-bird model are established, and the stability of solutions of the model is discussed by the ecological reproduction index , specifically, mistletoes go extinct when , and mistletoes coexist with birds when . Moreover, we show that network weights can induce changes of instantaneous dynamics of birds or mistletoes by the matrix perturbation method. By assuming that the weighted network is a river network and a star network, we simulate the extinction of mistletoes and the coexistence of mistletoes with birds, respectively.
基于槲寄生的斑块状栖息地和槲寄生与鸟类之间的互利关系，我们提出了一个基于加权网络的槲寄生-鸟类模型，该模型由离散拉普拉斯算子描述。在不考虑槲寄生的情况下，通过一个阈值参数来研究鸟类模型的动力学。在鸟类持续存在的前提下，建立了槲寄生-鸟类模型解的存在唯一性，并通过生态繁殖指数 讨论了模型解的稳定性，具体地说，当 时槲寄生灭绝，当 时槲寄生与鸟类共存。此外，我们通过矩阵扰动方法表明，网络权重可以引起鸟类或槲寄生瞬时动力学的变化。通过假设加权网络是一个河网和一个星形网络，我们分别模拟了槲寄生的灭绝和槲寄生与鸟类的共存。
