【摘要】 该文首先提出了一类带有经济效益的时滞分数阶微分-代数捕食-被捕食系统.利用稳定性理论,得到了在零经济收益条件下,系统的正平衡点是局部渐近稳定的;在正经济收益条件下,时滞产生Hopf分岔的充分条件.最后借助于数值模拟验证了理论的正确性,并进一步讨论了分数阶阶数、经济收益和时滞对系统稳定性的影响.更多还原

【Abstract】 A fractional differential-algebraic biological economic system with harvest and time delay is firstly proposed and investigated in this paper.By using the Hopf bifurcation theory,some sufficient conditions for the existence of Hopf bifurcation induced by delay are obtained.The results show that in the case of zero economic profit,the biological equilibrium point of the system is asymptotically stable.Under positive economic profit condition,the system produces limit cycles at the positive equilibrium point as the delay increases through a certain threshold.It is found that fractional exponent,economic interest and delay can affect the other dynamic behavior of the system through some numerical simulations.更多还原