Nonlinear behavior of the socio-economic dynamics for lake eutrophication control

To succeed in combating lake eutrophication, cooperation of local inhabitants, small factories, and farmers in reducing phosphorus discharge, is very important. But the willingness of each player to cooperate would depend on the cooperation of other players and on the level of environmental concern of the society in general. Here we study the integrated dynamics of people's choice of behavior and the magnitude of eutrophication. Assumptions are: there are a number of players who choose between alternative options: a cooperative and environment-oriented option is more costly than the other. The decision of each player is affected by "social pressure" as well as by economical cost of the options. The lake pollution increases with the total phosphorus released, and a high pollution level in the lake would enhance the social pressure. The model includes a positive and a negative feedback loops which create diverse dynamical behavior. The model often shows bistability - having an equilibrium with a high level of cooperation among people and clean water, and the other equilibrium with low cooperation and polluted water, which are simultaneously stable. The model also shows fluctuation between a high and a low levels of cooperation in alternating years, cycle with a longer periodicity, or chaotic fluctuation. Conservatism of people stabilizes the system and sometimes helps maintaining cooperation. The system may show unexpected parameter dependence - the improved phosphorus removing efficiency might make water more polluted if it causes the decline in the environmental concern and cooperation among people. (C) 2006 Elsevier B.V. All rights reserved.

为了成功应对湖泊富营养化问题，当地居民、小工厂和农民在减少磷排放方面的合作至关重要。但是，每个参与者合作的意愿将取决于其他参与者的合作情况以及整个社会对环境的关注程度。在此，我们研究人们行为选择的综合动态以及富营养化的程度。假设如下：有若干参与者在不同的选择之间进行抉择：一种合作且注重环境的选择比其他选择成本更高。每个参与者的决策受到“社会压力”以及选择的经济成本的影响。湖泊污染随着总磷释放量的增加而加剧，湖泊中较高的污染水平会增强社会压力。该模型包含一个正反馈回路和一个负反馈回路，它们产生了多样的动态行为。该模型常常呈现出双稳态——一种平衡是人们之间高度合作且水质清洁，另一种平衡是合作程度低且水质污染，这两种平衡同时稳定。该模型还显示出合作程度在不同年份高低交替的波动、周期较长的循环或混沌波动。人们的保守性使系统稳定，有时有助于维持合作。该系统可能表现出意想不到的参数依赖性——如果提高除磷效率导致人们对环境的关注和合作下降，那么可能会使水质更污染。（C）2006爱思唯尔有限公司。保留所有权利。