双时滞水体富营养化生态模型的稳定性与Hopf分支分析

Stability and Hopf Bifurcation Analysis of Eutrophication Ecological Model with Two Time Delays

研究了双时滞水体富营养化生态模型.从对模型特征方程根的分布分析入手,讨论了模型平衡点的稳定性,确定了模型的线性稳定性区域,发现当模型中的时滞经过一系列临界值时,模型在平衡点附近经历了Hopf分支.最后,数值模拟验证了理论结果.

The mathematical model of eutrophication ecological model with two time delays is studied. The stability of the equilibrium is discussed by analyzing the distribution of the solution of the characteristic equation and the regions of linear stability of equilibrium are given. It is found that the Hopf bifurcation is exist when the delay passes through a sequence of critical values. In the end, some numerical simulations are carried out to support the analytic results.