Dynamicalanalysis Of Land Model With Holling ? Land Reclamation Rate

Currently,land use and land cover change(LUCC)is the hot topic of global change study.With the rapid development of economic and urbanization,land resources are facing with the pressures of resource utilization and ecological protection.In this paper,land resources can be classified and we can build the dynamic model to understand of land-use change scientifically and develop a reasonable strategy to control land-use change.It is of great significance to promote the rational use of land resources.Firstly,In this paper,according to the condition that our country has less land than people,we consider the restriction of population density and introduce the Holling functional response function to describe land reclamation rate.The mathematical model with Holling ? land reclamation rate can be built according to the infectious disease model.Through the theory of differential equations,the positive equilibrium point and the basic reproductive rate are given in this paper,we prove that the positive equilibrium point is locally asymptotically stable through the Hurwitz theorem.By Lyapunov-Lasalle invariant theorem,we can conclude that the positive equilibrium is locally asymptotically stable.Secondly,time delay is a common phenomenon in the evolution of land.Based on the analysis of the evolution of land in recent years,this paper introduces the time delay to study the evolution of land.The equilibrium point is given and the stability is proved through the theory of the delay differential equation.Based on the Hopf bifurcation theorem,we analyze the existence of Hopf bifurcation.Finally,numerical simulations are also carried out to get out the trend of the land use.And we can discusses the influence on the stability of the evolution of land reclamation capacity.In order to make full use of unused land,we can construct the unused land into housing,factories,commercial land in the no time delay model.The wasteland can also be reclaimed to the land land for agriculture.Furthermore,we can appropriately increase the grassland's reclamation for the effective use of land.In thetime delay model we analyze the existence of Hopf bifurcation of the land use change,this explains the periodic change of the land area in China in recent years.