Abstract
This study is devoted to considering dynamic properties of an environmental protection expenditures model for protected areas (PAs) with two delays. It presents an improved understanding of relationship among tourism, environment, and capital stock in PAs and provides a sustainable strategy to keep the balance between them. The model considers the interactions among environmental resource , visitors , and capital stock in PAs. The tourism income is used partly to increase the capital stock and partly to protect the environment. In this paper, time delays and are introduced into the system. The technique of stability crossing curves for two delays is proposed to analyze the occurrence of Hopf bifurcation. Numerical simulations are performed for understanding the analytical results. The results show that under some parameter conditions, the share of total revenue generated by tourism user fees for environmental protection is related to delays and . Moreover, the environment and the capital stock can be maintained persistently if time delay is not too large.
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