A focus on long-run sustainability of an impulsive switched eutrophication controlling system based upon the Zeya reservoir

In this paper, within the framework of ordinary differential equation and eutrophication ecological theory, long-run sustainability of an impulsive switched eutrophication controlling system based upon the Zeya reservoir is studied analytically and numerically. A key advantage of the impulsive switched eutrophication controlling system is that it can be quite accurate to better describe the influence mechanism of some key factors during eutrophication controlling process, which enables a systematic and logical procedure for fitting eutrophication system to real monitoring data. Mathematical theoretical works have been pursuing the investigation of some conditions for all species persistence, which can deduce a standard parameter control relationship and in turn can provide a theoretical basis for the numerical simulation. Numerical analysis indicates that the theoretical results are correct and the long-run substainability of the impulsive switched eutrophication controlling system mainly depends on some critical parameters. It should also be stressed that the values of some critical parameter can be determined by a standard parameter control relationship. In addition, it is successful to show that the standard parameter control relationship maybe be used as an explicit threshold function to judge the long-run sustainability of eutrophication controlling process for the Zeya reservoir. Finally, all these results are expected to be of use in the study of the dynamic complexity of eutrophication ecosystems.