Stability and Bifurcation Analysis of an Environmental Protection Model with Two Delays
Abstract
This paper is devoted to studying an environmental protection model with two delays. The model considers the interactions among visitors V, environmental resource E, and capital stock K in protected areas. The tourism user fees obtained from visitors are partly used as an environmental expenditure and partly as the increment of capital stock. The spread delay τ1 and the protection delay τ2 are introduced. The stability switching cures for the two delays are used to investigate the stability of the equilibrium and the occurrence of Hopf bifurcation. The bifurcating directions are determined. Numerical simulations are given to illustrate the results. In this model, the quality of the environmental resource is related closely to the environmental expenditure, where the more the environmental expenditure, the better the quality of the environmental resource. This result will be useful for the protection of the protected areas.
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