The coupled dynamics of human socio-economic choice and lake water system: the interaction of two sources of nonlinearity

We study a mathematical model for the coupled dynamics of human socio-economic choice and lake water system. In the model, many players choose one of the two options: a cooperative and costly option with low phosphorus discharge, and an economical option with high phosphorus discharge. The choice is affected by an economic cost, a social concern about water pollution, and a conformist tendency. The pollution level in the lake is determined by total phosphorus discharge by the players, the sedimentation and the outflow of phosphorus, and the recycling of phosphorus from the sediment. The model has two sources of nonlinearity: the cooperation level tends to be bistable due to conformist tendency of people (social hysteresis) and pollution level tends to be bistable because phosphorus recycling occurs faster in more eutrophic lakes (ecological hysteresis). The combination of these two sources may cause multiple stable equilibria or oscillations with a long periodicity. Small economic cost and strong social concern about pollution level can decrease the pollution level, but may not be very effective in enhancing the cooperation level. In contrast, strong conformist tendency produces a stable state with a high cooperation level and a low pollution level. We discuss implications of these results to the water quality management.