本研究提出一个具有时滞的分数阶生态流行病系统,着重分析引入时滞对系统的动力学影响。以时滞作为分岔参数,利用线性化方法和Laplace变换法分析系统在正平衡点附近发生Hopf分岔的条件,推导出时滞临界值的计算式。研究表明,当时滞穿越相应的临界值时,系统将失去稳定性,并发生Hopf分岔。同时发现随着系统阶次的增加,系统分岔也会提前发生。最后,通过数值仿真验证理论分析的正确性,以及分数阶次的变化对系统稳定域的影响。

This paper proposed a fractional eco-epidemic system with time delays and focused our analysis on the kinetic effects of introducing time delays on the system. Taking the time delay as the bifurcation parameter, it first analyzed the conditions of Hopf bifurcation near the positive equilibrium point by using the linearization method and the Laplace transform method, and then derived the formula of the critical value of the time delay. It is shown that when the delay passes the corresponding critical value, the system will lose stability and Hopf bifurcation will occur. With the increase of the system order, the system bifurcation occurs earlier. Finally, we conducted numerical simulations to validate the theoretical analysis and effect of fractional order changes on the stability domain of the system.