一类具有两时滞的恒化器模型的分支研究

Bifurcation Analysis of a Chemostat Model with Two Delays

研究了一类具有离散和分布时滞的恒化器模型,得到了时滞对系统稳定性的影响:当时滞小于临界值时,正平衡点是局部渐近稳定的;当时滞经过临界值时,时滞破坏了正平衡点的稳定性,Hopf分支产生了一族经过正平衡点的周期解,并通过数值仿真验证了结果.

A chemostat model with a discrete and a distribution delays is investigated. The effect of the delay for the system is obtained. When the delay as bifurcation parameter is less than the threshold, the positive equilibrium is locally asymptotic stable. When the delay crosses the threshold, the hopf bifurcation destroys the stability of the positive equilibrium, a family of periodic solution is produced by Hopf bifurcation. Finally, the results are carried out by the numerical simulation.