Dynamic Analysis Of Green Development System Under The Background Of Environmental Tax

With green development becoming a global movement,environmental tax has been adopted by many governments to promote green development.However,few studies have rigorously quantified the complex interactions between environmental tax and green development.This paper establishes a dynamical system model to quantitatively analyze the evolution regulations of green development under different scenarios in China.Futhermore,the dynamic behaviors and hyperchaos control of the system are studied using the nonlinear dynamic theory.Results are beneficial to recognize the magnanimity of influence of various factors on China's green development and take reasonable measures to promote green development.Contents of this study are as follows:(1)The evolution paths of green development in China are analyzed by the dynamical system model.Firstly,the core of green development is to improve resource utilization and reduce pollution emission while without slowing economic growth.Therefore,this paper selects resource consumption,GDP,pollution emission,and environmental tax as state variables to establish a fourdimensional model,that is,green development dynamical system.Secondly,the stability of the system is studied through the dissipative analysis and Routh-Hurwitz criterion.Moreover,the Lyapunov exponent spectrum and bifurcation diagram show that the system has complex dynamic behaviors: chaos,limit cycle,and equilibrium point.Then,taking China as an example,the required data are obtained based on the China Statistical Yearbook.The underlying data are pre-processed via Analytic Hierarchy Process,and the actual parameters are identified using genetic algorithm.Finally,the evolution of the quantitative indicators is used to reflect the evolutionary characteristics of green development.In order to quantify the impact of environmental tax on green development,three quantitative indicators of economic growth,resource intensity,and pollution intensity are introduced.The results show environmental tax can improve green development to a certain extent.In addition,when the environmental tax is levied,strong government control,positive consumer awareness,and advanced technology level can stimulate economic growth,reduce pollution intensity,and control resource intensity,while government control has a more pronounced effect.(2)The dynamic behaviors and hyper-chaos control of green development dynamical system are studied.First of all,this paper performs a series of dynamic analysis of the system: equilibrium point,stability,dissipation,Lyapunov exponent,and bifurcation.The existence of chaos is verified by the Lyapunov exponent spectrum and bifurcation diagram.Furthermore,two positive Lyapunov exponents and the value of Lyapunov dimension indicate that the system exists hyper-chaos.Next,this thesis selects adaptive control,self-linear feedback control,and dislocation linear feedback control to suppress the hyper-chaotic phenomenon of the system.According to the Lyapunov stability theorem,the hyper-chaotic phenomenon can be controlled to an unstable equilibrium point under a constructed adaptive controller and adaptive law.Theoretical analysis shows that all three control methods can achieve the supremacy of hyper-chaotic phenomenon.Last,the numerical simulation also obtains the same results that the speed of adaptive control is much faster than the other two methods.However,the design of adaptive controller is relatively complicated.Therefore,we still have to choose an appropriate control method according to actual situations.