Dynamics Analysis Of Forest Turnover Model Under Three Types Of Tending Management Measures

The management and cultivation of foresty ecosystem has been one of the most important topics of human concern.Nowadays,due to the development of social economy and the increase of population,the forest management ”emphasizes harvesting rather than cultivation”,resulting in insufficient total forest resources and a sudden decrease of forest area.To address this issue,this paper takes red pine forest as an example,considers the relationship between young red pine trees and parent trees,constructs three types of tree turnover model under different tending management measures,and studies the corresponding dynamics.The structure of this paper consists of the following four parts:In the first chapter,the introduction introduces the current status and background of forestry ecosystem management,and gives the current work done by researchers and some basic theoretical knowledge covered in this paper.In the second chapter,under the background of excessive density of parent trees,a continuous model of young-parent red pine trees with a constant number of thinning parent trees is constructed.The positivity and boundedness of the system,the existence and stability of positive equilibrium points,the existence of Hopf branch and saddle-node branch are studied,finally,the corresponding numerical simulation is given to verify the theory.The results show that when the constant logging intensity is small,the young trees can coexist with the parent trees,with the increase of the logging intensity,the limit cycle and Hopf branching phenomenon will appear,when the constant logging intensity is too large,saddle-node branch will be generated,and also lead to extinction of the parent trees.In the third chapter,based on the second chapter,in order to avoid the extinction of the parent trees due to over-lumbered,the state feedback control measures are used to parent trees,a young-parent red pine trees model with state feedback control is constructed.Using methods such as the successor function and the class Poincar’e criterion,the existence and orbit asymptotic stability of the order-1 periodic solution of the system in the absence of limit cycle are investigated,as well as the existence of the order-1 periodic solution and the order-2 periodic solution in the presence of limit cycle.Finally,the results of numerical simulation show that the state feedback control measures can effectively promote the growth of both young trees and parent trees,and maintain a healthy turnover of the forest.In the finally chapter,considering the phase of thinning parent trees,the Filippov model of young-parent red pine trees with switching effect is constructed,the sliding mode dynamic properties of the system are investigated,in addition,under seven different scenarios,the effect of threshold on the global dynamic of the Filippov model is also discussed.The results of numerical simulation show that by selecting appropriate control threshold,the biomass of parent trees can be effectively reduced to achieve high growth of young trees,and provide a theoretical reference for the rational selection of control strategies in practice.