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In recent years, the environmental problem caused by economic development has been an important issue all over the world. The traditional analysis of environmental pollution often relies on the endogenous growth model, where environmental pollution is treated as a factor that influences capital and population. In this paper, we develop a nonlinear model that integrates economic growth, technological progress, resource consumption, and environmental pollution to explore the dynamic mechanisms of economic growth under environmental constraints. We first prove the non-negativity of the model’s solutions, followed by establishing their boundedness using a Lyapunov function. Additionally, we investigate, for the first time, the tipping point of a key parameter within the model related to environmental pollution, demonstrating that neglecting environmental pollution renders economic growth unsustainable and can lead to collapse. The study also examines two distinct types of environmental governance aimed at controlling pollution, computing the tipping points associated with economic growth under each governance strategy. Our findings highlight the critical role of green production methods in sustaining economic growth. Finally, we analyze how initial conditions and random disturbances affect the steady-state of economic growth, revealing that initial levels of capital and technological skill can determine the system’s steady-state, while stochastic shocks can alter tipping points and push the system away from stability.
Li et al. (Sun,) studied this question.