Types Of Non-autonomous Population Dynamics Model

Population dynamic model, a major component of biological mathematical model, is now widely receiving attention from peer scholars both at home and aboard. This paper, based on previous research, makes a deeper and wider discussion on heteronomy population dynamic model, including the research of single-species model with pulse diffusion, the research of two competitive species model with Holling II functional response and pulse culling, and the research of Lotka-Volterra competition model with saturation rate and artificially harvesting of economical birds.The main contents in this paper can be summarized as follows:In section 1, we introduce the ecological background of this paper. Then, it is given that some research conclusion recently about nonautonomous population dynamic model. Finally, we investigate our research work.Pulse diffusion effectively reflect the spread of migratory birds between patches. A single-species nonautonomous Gompertz model with pulse diffusion is proposed in Section 2. We obtain that the positive periodic solution of the model is globally asymptotically stable if the overall growth rate is larger than zero, whereas the species will be extinct if the overall growth rate is equal or lesser than zero.In Section 3, we consider two competing species: rare migratory bird and economical bird, and investigate a nonautonomous two species competitive model with Holling-type II functional response, which the pulse culling is incorporated. By utilizing analyzing method, sufficient and realistic conditions on permanence, extinction of the two species, existence of positive periodic solution and the global attractivity of semi-trivial periodic solution are established. The theoretical results are confirmed by numerical simulations.In Section 4, we study the dynamics of competing species: susceptible migratory bird, infected migratory bird and economical bird, and investigate a nonautonomous two species competitive model with saturation incidence and artificially harvesting. Under the reasonable assumptions, sufficient conditions for the permanence and extinction of the disease are obtained. Moreover, the global attractivity of the model is discussed by constructing a Liapunov function. To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.