Soft Computing

, Volume 22, Issue 16, pp 5311–5321 | Cite as

Dynamic analysis for Governance–Pollution model with education promoting control

  • Jiaorui LiEmail author
  • Siqi Yu


The pollution and its governing problem have drawn the world’s extremely attention. To study the sensitivities of different governing methods, we formulate a dynamic system which is analyzed through two cases of noncooperation and with-cooperation among the enterprises and the government. The dynamic system describes the influences caused by the pollution control investment, the time delay of the abatement investment and the degree of the cooperation between the government and the enterprise. At last, we solve the optimal control problem based on turnpike theorem. It is shown that the economic output in a country could affect the steady state of the pollutant emissions. Moreover, the threshold value of time delay that the society can accept on the pollution control investment is non-integer. Furthermore, the environmental policies’ implementation could remedy the polluting weakness of the countries with higher economic outputs. Finally, we solve the optimal control problem in the G–P model through education promoting.


Pollutant emissions Cooperation Stability analysis Turnpike theorem 


Compliance with ethical standards

Conflicts of interest

Authors Jiaorui Li and Siqi Yu declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


This study was funded by National Natural Science Foundation of China under Grant Number [Grant Numbers: 11572231] and “Yan Ta” Scholars Project of Xi’an University of Finance and Economics.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of StatisticsXi’an University of Finance and EconomicsXi’anPeople’s Republic of China

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