Stability and Optimal Control of a Nonlinear Tourism--Environment Dynamic System for Sustainable Tourism Management

Abstract

The rapid growth of the tourism sector has generated several challenges, including increased tourist pressure, environmental degradation, and economic imbalances. These challenges can be addressed by developing mathematical models for sustainable tourism. This study develops a nonlinear dynamic model to describe the interactions among tourist numbers, economic growth, investment in the tourism sector, and environmental quality within the framework of sustainable tourism management. The model is formulated as a system of nonlinear ordinary differential equations that accounts for the impact of environmental quality on the growth of the tourism and economic sectors. In this study, a dynamic analysis was conducted, including the formulation of a well-posed model, the determination of equilibrium points, and a local stability analysis in their vicinity. Next, to develop an effective tourism system management strategy, an optimal control approach was employed using two control variables. The results of the numerical simulation show that the model can qualitatively represent the dynamics of a sustainable tourism system and that the application of optimal control can improve the balance among the number of tourists, economic growth, investment, and environmental sustainability.