Dynamic Behaviors Analysis Of A Carbon Price Evolution System

With the integration of the global economy,the economic growth at the cost of seriously destroying the ecological environment poses a great challenge to sustainable development.Countries are gradually taking measures to save energy and reduce emissions,and realize that the carbon market is the least-cost tool to reduce carbon emissions.Starting from the complex interactions among carbon price,energy price and economic growth,this paper establishes a dynamical system model to analyze the evolutionary trends of carbon price under different scenarios in China,and adopts two different control methods to control the chaos of the system to a stable equilibrium state.The research results are helpful to analyze the development trends in the carbon price in the mid-term to long-term,and put forward reasonable low-carbon development strategies.Firstly,this paper discusses the evolutionary trends of the carbon price from the perspective of nonlinear dynamical system.Clarify the complex dynamic relationships among carbon price,energy price,and economic growth,a three-dimensional nonlinear dynamical system model is constructed,namely the carbon price dynamical system.The number and types of equilibrium points in the system are analyzed.The RouthHurwitz criterion and dissipation are used to study the stability of the system,and the nonlinear dynamic behaviors of the system are analyzed.Taking China as an example,the required sample data is obtained based on the public database and statistical yearbooks,and the actual parameters of the system are identified with the aid of the genetic algorithm,and then the sensitivity of the system parameters is analyzed to explore the evolutionary trends of the carbon price in different actual scenarios.The research results show that the carbon price is positively correlated with energy price as well as energy price policy.Besides,the level of the carbon price is negatively correlated with government control in the short term and positively correlated in the long term.Secondly,the chaos control of the carbon price dynamical system is studied.Based on the constructed carbon price dynamical system,a proper time-delayed feedback controller is introduced to control the chaos of the carbon price system.By analyzing the distribution of the corresponding characteristic roots of the time-delayed system at the equilibrium point,the local stability of the system and the existence of Hopf bifurcation are obtained.The conclusions acquired by numerical simulations are consistent with theoretical analysis.Similarly,a linear feedback controller is introduced,and the stability of the controlled system is analyzed through the Route-Hurwitz criterion.It is found that the chaotic system can be quickly suppressed to the equilibrium point when the feedback gain is in the stable range.