Based on the predator–prey system with a Holling type functional response function, a diffusive predator–prey system with digest delay and habitat complexity is proposed. Firstly, the stability of the equilibrium of diffusion system without delay is studied. Secondly, under the Neumann boundary conditions, taking time delay as the bifurcation parameter, by analyzing the eigenvalues of linearized operator of the system and using the normal form theory and center manifold method of partial functional differential equations, the effect of time delay on the stability of the system is studied and the conditions under which Hopf bifurcation occurs are given. In addition, the calculation formulas of the bifurcation direction and the stability of bifurcating periodic solutions are derived. Finally, the accuracy of theoretical analysis results is verified by numerical simulations and the biological explanation is given for the analysis results.

基于具有Holling型功能响应函数的捕食者-猎物系统，提出了一种具有消化延迟和栖息地复杂性的扩散捕食者-猎物系统。首先研究了无延迟扩散系统平衡的稳定性。其次，在诺依曼边界条件下，以时滞为分岔参数，通过分析系统线性化算子的特征值，利用偏泛函微分方程的范式理论和中心流形方法，研究时滞对稳定性的影响研究了系统的结构，并给出了发生 Hopf 分岔的条件。此外，推导了分岔方向和分岔周期解稳定性的计算公式。最后，