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In this paper, a novel three-dimensional environmental quality dynamic system is introduced. Bayesian estimation was used to calibrate environmental quality variables, and Genetic algorithm (GA) optimized Levenberg-Marquardt Back Propagation (LM-BP) neural network method was used to effectively identify the system parameters for calibration of various variables and official data. The studies found that the effect of increasing investment in environmental protection on energy intensity and environmental quality is not obvious, and it also aggravates the economic instability. Adjustment of peak parameters of pollution emissions can accelerate the evolution of energy intensity and environmental quality to a stable speed and eventually stabilize with a certain value. But if the peak value of pollution emissions reaches too early, it will pose a certain threat to the environment. Although the speed of ecological environment self-repair is increased, it cannot effectively reduce energy intensity, improve environmental quality, and maintain economic growth; it can control the stability of the control system or effectively control pollution. Therefore, in order to improve the environmental quality, we need to take more measures in parallel, use more means and resources for environmental governance, and ultimately achieve “win-win” between environmental quality and economy.

A novel four-dimensional energy, economic, and environmental (3E) under energy reduction constraints chaotic system is proposed. The acquisition of environmental quality data is the key to this paper. During the course of the study, we used Bayesian estimation algorithm to calibrate the environmental quality. Based on the official data, the Levenberg–Marquardt backpropagation neural network method was optimized by genetic algorithm to effectively identify the parameters in the 3E system. The research results show that although increasing energy reduction inputs can improve environmental quality, the effect on energy intensity and overall stability of the system is not obvious. When polluting input in the ecological environment system affects its maximum capacity, the environmental system collapses (i.e., the ecological system can no longer purify the environment through the self-circulation process and will eventually die out). Therefore, it is necessary to correctly grasp the ecological environment protection and the relationship between economic developments and explore synergies to promote ecological priorities and green development new ideas.

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