Nonlinear differential equations and their application to evaluating the integrated impacts of multiple parameters on the biochemical safety of drinking water.

The present study aimed to narrow such gaps by applying nonlinear differential equations to biostability in drinking water. Biostability results from the integrated dynamics of nutrients and disinfectants. The linear dynamics of biostability have been well studied, while there remain knowledge gaps concerning nonlinear effects. The nonlinear effects are explained by phase plots for specific scenarios in a drinking water system, including continuous nutrient release, flush exchange with the adjacent environment, periodic pulse disinfection, and periodic biofilm development. The main conclusions are, (1) The correlations between the microbial community and nutrients go through phases of linear, nonlinear, and chaotic dynamics. Disinfection breaks the chaotic phase and returns the system to the linear phase, increasing the microbial growth potential. (2) Post-disinfection after multiple microbial peaks produced via metabolism can increase disinfection efficiency and decrease the risks associated with disinfectant byproduct risks. This can provide guidelines for optimizing the disinfection strategy, according to the long-term water safety target or a short management. Limited disinfection and ultimate disinfection may be more effective and have low chemical risk, facing longer stagnant conditions. (3) Periodic biofilm formation and biofilm detachment increase the possibility of uncertainty in the chaotic phase. For future study, nonlinear differential equation models can accordingly be applied at the molecular and ecological levels to further explore more nonlinear regulation mechanisms.