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<p>Sustainable reservoir operation increasingly depends on understanding the coupled interactions between hydrological processes and governance performance. This study develops a nonlinear dynamical model to investigate the joint evolution of reservoir water volume and management quality under physical losses and institutional constraints. The mathematical formulation incorporates inflow, designed outflow, leakage, evaporation, and illegal withdrawals, where each loss component is represented as a nonlinear function of water volume and governance level. Analytical examination of the system establishes positivity, boundedness, and the existence of a unique equilibrium point. Local and global asymptotic stability conditions are obtained through Jacobian analysis, Lyapunov’s direct method, and LaSalle’s invariance principle. The numerical simulations, performed under five representative scenarios, demonstrate the system’s sensitivity to inflow reduction, decreasing management effort, and intensified illegal withdrawals, any of which may lead to instability or reservoir depletion. Conversely, improved governance and stronger enforcement significantly enhance the system’s long-term resilience and stabilize the reservoir at higher steady-state volumes. The results highlight the critical role of management effectiveness in mitigating physical losses and ensuring the sustainable operation of water storage systems. The presented framework provides a flexible decision-support tool for evaluating reservoir response to combined hydrological and socioinstitutional pressures.</p>

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Modeling and stability of reservoir systems under physical losses and governance

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • M. Tahavor,
  • K. Laei,
  • M. A. Bafghi

摘要

Sustainable reservoir operation increasingly depends on understanding the coupled interactions between hydrological processes and governance performance. This study develops a nonlinear dynamical model to investigate the joint evolution of reservoir water volume and management quality under physical losses and institutional constraints. The mathematical formulation incorporates inflow, designed outflow, leakage, evaporation, and illegal withdrawals, where each loss component is represented as a nonlinear function of water volume and governance level. Analytical examination of the system establishes positivity, boundedness, and the existence of a unique equilibrium point. Local and global asymptotic stability conditions are obtained through Jacobian analysis, Lyapunov’s direct method, and LaSalle’s invariance principle. The numerical simulations, performed under five representative scenarios, demonstrate the system’s sensitivity to inflow reduction, decreasing management effort, and intensified illegal withdrawals, any of which may lead to instability or reservoir depletion. Conversely, improved governance and stronger enforcement significantly enhance the system’s long-term resilience and stabilize the reservoir at higher steady-state volumes. The results highlight the critical role of management effectiveness in mitigating physical losses and ensuring the sustainable operation of water storage systems. The presented framework provides a flexible decision-support tool for evaluating reservoir response to combined hydrological and socioinstitutional pressures.