School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China.
School of Management, Shanghai University of International Business and Economics, Shanghai 201620, China.
Math Biosci Eng. 2023 May 26;20(7):12625-12648. doi: 10.3934/mbe.2023562.
We incorporate the fear effect and the maturation period of predators into a diffusive predator-prey model. Local and global asymptotic stability for constant steady states as well as uniform persistence of the solution are obtained. Under some conditions, we also exclude the existence of spatially nonhomogeneous steady states and the steady state bifurcation bifurcating from the positive constant steady state. Hopf bifurcation analysis is carried out by using the maturation period of predators as a bifurcation parameter, and we show that global Hopf branches are bounded. Finally, we conduct numerical simulations to explore interesting spatial-temporal patterns.
我们将捕食者的恐惧效应和成熟阶段纳入扩散型捕食者-猎物模型中。得到了常数稳定态的局部和全局渐近稳定性以及解的一致持续性。在某些条件下，我们还排除了空间非均匀稳定态的存在以及从正的常数稳定态分岔出的稳定态分岔。利用捕食者的成熟阶段作为分岔参数进行了 Hopf 分岔分析，结果表明全局 Hopf 分支是有界的。最后，我们进行了数值模拟以探索有趣的时空模式。
