分数阶双时滞传染病系统的捕食者-食饵模型动力学

Dynamics of a fractional predator-prey model with infectious disease and double time delays

为了研究分数阶传染病系统的动力学复杂性,提出一种具有双时滞分数阶生态传染病的捕食者-食饵模型,并探讨捕食者妊娠期和传染病潜伏期对系统动力学的影响.首先初步分析系统平衡点的存在性,然后基于系统的特征方程推导出模型的稳定性和Hopf分岔条件,并确定2种不同时滞引起的分岔判据.数值仿真结果表明,当时滞大于分岔阈值时,系统失去稳定性且产生Hopf分岔.

In order to study the dynamics complexity of fractional infectious disease systems, a fractional predator-prey model of fractional infectious disease with double delays is proposed and the effects of predator gestation period and infectious disease on system dynamics are investigated. Firstly, the existence of equilibrium point of the system is analyzed. Then, based on the characteristic equation of the system, the conditions of the stability and Hopf bifurcation for the fractional predator-prey model are derived, and two bifurcation criteria caused by different time delays are determined. Numerical simulation results show that when the hysteresis is greater than the bifurcation threshold, the system loses stability and a Hopf bifurcation emerges.