Modeling heavy metal water-sediment partitioning using a nonlinear bifurcation approach

Abstract

Heavy metal transport between the water column and sediment is commonly described using linear or empirical relationships, which may not capture nonlinear feedback mechanisms and abrupt changes in contamination states. In this study, we proposed a nonlinear cubic equilibrium model for describing metal partitioning between water and sediment and for identifying critical transition conditions associated with bifurcation behavior. The proposed model established a nonlinear relationship between the input metal concentration in water I_i and the accumulated sediment concentration C_i. Using experimental data for copper (Cu) and nickel (Ni) transport from the literature data, model parameters were estimated by the least-squares method. The obtained response curves exhibited an S-shaped structure, indicating the existence of multiple equilibrium states, bistability, and hysteresis. Fold points obtained from the condition d I_i/d C_i=0 defined critical thresholds at which saddle-node bifurcations occur and abrupt transitions between contamination states become possible. The bifurcation analysis with respect to the nonlinear parameter p_i further identified critical values separating bistable and monostable regimes. The results demonstrated that Cu and Ni systems may exhibit history-dependent behavior, where the sediment contamination level is not determined solely by the current pollution input but also by the previous evolution of the system. The proposed framework extends conventional pollutant transport models by incorporating nonlinear dynamics, multistability, and regime-shift mechanisms. It provides a mathematical basis for identifying tipping points in water-sediment contamination systems and offers a potential tool for assessing environmental risks associated with sudden changes in metal accumulation. The main contribution of this work is the demonstration that nonlinear bifurcation analysis provides insight into critical states, multistability, hysteresis, and regime transitions in water-sediment contamination systems, extending conventional concentration-based approaches toward a deeper understanding of nonlinear environmental dynamics.

Keywords

heavy metal transport / water-sediment interaction / nonlinear cubic model / bifurcation analysis / saddle-node bifurcation / hysteresis / multistability / tipping point / regime shifts / sediment contamination

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