Abstract

Spatiotemporal variability in water quality is often expressed so clearly that the variance of the monitored parameters exceeds their average value. This circumstance substantially complicates water management. It is practically important and theoretically interesting to find any dynamic trends in the processes of natural water quality evolution. These trends are difficult to detect with a linear approach to the evolution of quality parameters that are random in nature, but it is possible to take into account the nonlinearity of natural aquatic systems. The nonlinear logistic rule derived in this way enables estimation of the composition of water as a function of the intensity of the processes of its pollution and self-purification. It is shown that an aquatic ecological system shows linear behavior only in the case of slow processes when its parameters approach certain stable (equilibrium) values. With an increase in the intensity of pollution and self-purification processes, cyclic fluctuations of the monitored parameter occur. Their amplitude remains small at a low rate of pollution and increases with an increase in the pollution rate or even is accompanied by bifurcations with a further transition to total chaos. This is an indication of the substantial nonlinearity of natural aquatic systems, which is manifested, in particular, as energy dissipation of ordered processes and as bifurcations, i.e., unexpected changes in controlled parameters. In this case, order parameter fluctuations that determine singular contributions to the controlled dynamic characteristics serve as influencing nonlinearity factors. The performed theoretical analysis is confirmed by the observational data, which show that the aquatic ecological system under study has a noticeable degree of organization. The water management efficiency can be improved by taking these circumstances into consideration.

中文翻译：

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水质演化动态模型

摘要

水质的时空变异性通常表达得如此清晰，以至于监测参数的方差超过了它们的平均值。这种情况使水管理大大复杂化。发现自然水质演变过程中的任何动态趋势具有实践意义和理论意义。这些趋势很难用线性方法来检测本质上随机的质量参数的演变，但可以考虑自然水生系统的非线性。以这种方式导出的非线性逻辑规则能够估计水的成分，作为其污染和自我净化过程强度的函数。结果表明，水生生态系统仅在缓慢过程的情况下，当其参数接近某个稳定（平衡）值时，才表现出线性行为。随着污染和自净化过程强度的增加，监测参数出现周期性波动。它们的幅度在低污染率下仍然很小，并随着污染​​率的增加而增加，甚至伴随着分叉，进一步过渡到完全混沌。这表明天然水生系统存在很大的非线性，特别是表现为有序过程的能量耗散和分叉，即受控参数的意外变化。在这种情况下，确定对受控动态特性的奇异贡献的阶参数波动用作影响非线性因素。所进行的理论分析得到了观测数据的证实，表明所研究的水生态系统具有明显的组织化程度。考虑到这些情况，可以提高水资源管理效率。