摘要
In this paper,a stochastic delayed differential algebraic predator-prey model with Michaelis-Menten-type prey harvesting is proposed.Due to the influence of gestation delay and stochastic fluctuations,the proposed model displays a complex dynamics.Criteria on the local stability of the interior equilibrium are established,and the effect of gestation delay on the model dynamics is discussed.Taking the gestation delay and economic profit as bifurcation parameters,Hopf bifurcation and singularity induced bifurcation can occur as they cross through some critical values,respectively.Moreover,the solution of the model will blow up in a limited time when delay τ>τ0.Then,we calculate the fluctuation intensity of the stochastic fluctuations by Fourier transform method,which is the key to illustrate the effect of stochastic fluctuations.Finally,we demonstrate our theoretical results by numerical simulations.
基金
This work was supported by the Natural Science Foundation of China(Grant Nos.11861065,11771373 and 11961066)
the Natural Science Foundation of Xinjiang Province of China(Grant No.2019D01C076)
The Doctoral innovation project of Xinjiang University(XJUBSCX-2017005)
the graduate research innovation project of Xinjiang Province(XJ2019G007)
the China Scholarship Council under a joint-training program at Memorial University of Newfoundland(201907010023).
