Dynamics of a mistletoe-bird model on a weighted network

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 \(R_0^m\) $R_0^m$ , specifically, mistletoes go extinct when \(R_0^m<1\) $R_0^m<1$ , and mistletoes coexist with birds when \(R_0^m>1\) $R_0^m>1$ . 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.