Optimal Harvesting Strategies For Timber And Non-timber Forest Products

Forest resources are renewable resources.Rational exploitation and utilization of forest resources is conducive to sustainable development of population and higher economic benefits.In this paper,based on the actual timber harvesting problem and the development status of timber and non-timber products in the forest,the combined timber and non-timber harvesting model with nonlinear harvesting terms is established.In the past,constant harvesting and proportional harvesting were used to solve timber harvesting problems,but constant harvest is not conducive to the protection and restoration of the population in the actual ecological environment,and the actual harvest can not be a simple linear harvest because there are many influencing factors.Therefore,this paper adopts nonlinear harvesting to establish a model,and use optimal control theory to study the optimal harvesting problem.The main research achievements of this paper are as follows:1.Establish and study the combined harvesting model of timber and non-timber with nonlinear harvesting and its optimal harvesting strategy.Based on the qualitative theory of ordinary differential equations,the dynamic behavior of the model is studied,and the existence and stability conditions of equilibrium point are proved.Secondly,in order to study the optimal harvest for timber and non-timber forest products,two optimal control problems for timber and non-timber with nonlinear harvest are emphatically analyzed: the optimal control problem only considers the economic benefit,and the optimal control problem considers the economic benefit and ecological benefit.The harvest effort is selected as the optimal control variable,and the optimal control strategy is obtained by using Hamilton function and Pontryagin maximum principle.At the same time,the optimal control problem is simulated numerically.By comparing the numerical results of the optimal harvesting strategy with nonlinear harvesting and proportional harvesting,the optimal harvesting strategy which can make the ecological benefits higher and more conducive to the sustainable development of the population is finally obtained.Combined with the sensitivity analysis of parameters,the relevant parameters which have great influence on the harvesting strategy were found out.2.Since insect pests in forests can increase the mortality of trees,ecological models are established considering the interaction between beetles and forest wood,and joint harvesting strategies for timber and non-timber forest products with nonlinear harvesting affected by beetles are studied.The harvest effort of timber and non-timber and the kill rate of beetles were selected as the optimal control variables,and the optimal harvest strategy with practical significance was given.