Sustainable Tourism Dynamics through Nonlinear Systems and Lyapunov Stability Analysis

Aims/ Objectives: This paper develops a nonlinear differential equation model to capture the dynamic interactions among economic performance, environmental conditions, social receptiveness, tourist volume, and cultural integrity within a tourism system. Study Design: The study utilizes Lyapunov stability theory to identify conditions under which the system can withstand disturbances and return to equilibrium. Place and Duration of Study: Department of Tourism and Hospitality Management and Department of Mathematical Sciences, Lagos State University of Science and Technology, Ikorodu, lagos, Nigeria; and Department of Mathematics, Anchor University, Ayobo, Lagos, Nigeria, between January 2025 and May 2025. Methodology: Boundedness analysis is conducted to ensure the model variables remain within realistic limits, reflecting the sustainability of tourism activities. Numerical simulations are used to validate the theoretical results and demonstrate how different parameters influence the system’s trajectory. Results: The findings underscore the importance of targeted policy measures, such as visitor quotas, sustainable investments, and community engagement, to support resilient and sustainable tourism development. Conclusion: The model provides insights into the sustainability of tourism activities and emphasizes the need for strategic interventions to maintain the long-term viability of tourism systems.