Abstract
<title>Abstract</title> <p>This study develops a nonlinear dynamical model of the coupled evolution of reservoir volume and governance quality, in which leakage, evaporation, and illegal-withdrawal losses are represented as nonlinear functions of both storage volume and management effectiveness. For the open-loop system, positivity, boundedness, and existence and uniqueness of an equilibrium are established, and local and global asymptotic stability are derived via Jacobian analysis, Lyapunov's direct method, and LaSalle's invariance principle. The model is then extended to a reinforcement-learning setting in which management effort is generated in closed loop by a policy trained under stochastic hydrological forcing, for which analogous existence, local-stability, and practical (input-to-state) stability results are derived. Numerical simulations across five scenarios show that the learned policy reduces cumulative control cost by 15--45\% relative to a fixed-effort baseline, at the cost of a higher frequency of near-depletion excursions in most cases. The results show that treating governance as an endogenous, dynamically evolving state, rather than an exogenous parameter, changes both the predicted long-term behavior of a reservoir and the design of policies to manage it, offering a decision-support framework for reservoirs under combined hydrological and institutional pressures.</p>