Stability and dynamics analysis of time delayed eutrophication ecological model based upon the Zeya reservoir

In this paper, within the framework of ordinary differential equation and eutrophication ecological theory, a time delayed eutrophication ecological model based upon the Zeya reservoir is studied analytically and numerically. A key advantage of time delayed term is that it can be quite accurate to describe food energy transformation mechanism, which enables a systematic and logical procedure for fitting eutrophication model to real monitoring data. Mathematical theoretical works have been pursuing the investigation of some stability conditions for the equilibria, which in turn provides a theoretical basis for the numerical simulation. Numerical analysis indicates that the time delayed term has an important role in complex dynamics using comparative analysis of the bifurcation diagram. It should also be stressed that chaos spontaneously appears with increase of a critical parameter for the system without time delayed term. In addition, it is successful to show that the time delayed term may be a critical factor for complex dynamics, which can directly suppress the emergence of chaos and promote the system to enter into a steady state. All these results are expected to be useful in the study of the dynamic complexity of eutrophication ecosystems.