具有时滞的生态-流行病SI模型的稳定性和HoPf分支及其数值模拟

摘要

A delayed SI Predator-Prey ePidemiological system with disease sPreading in Prey PoPula-tion is considered in this PaPer. Using the method of characteristic equation the existence and stabili-ty of the equilibria are analyzed. Positive equilibrium is locally asymPtotically stable when time delayτ<τ0 . While a loss of stability by a HoPf bifurcation can occur as the delays increase. the results are showed by numerical simulation that the qualities of the Positive equilibrium are in accordance with the theory analysis.%考虑一类含有时滞的食饵染病的生态-流行病SI模型，主要利用特征根法讨论了平衡点的存在性及其稳定性，证明了当时滞τ<τ0时，正平衡点是局部渐近稳定的，随着时滞增加，正平衡点由稳定变为不稳定，系统在正平衡点附近产生HoPf分支，通过数值模拟表明正平衡点的性质与理论分析一致。