Abstract In this paper, the dynamics of a general predator-prey system with diffusion and stage structures are investigated. Under some assumptions, the stability of positive steady state and the existence of local Hopf bifurcation are obtained by analyzing the distribution of eigenvalues. Moreover, the global existence of positive periodic solution is established by using the global Hopf bifurcation result of Wu. Finally, an example and some numerical simulations are carried out for illustrating the theoretical results.

中文翻译：

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具有扩散和阶段结构的一般捕食者-猎物系统的全局 Hopf 分叉

摘要 本文研究了具有扩散和阶段结构的一般捕食者-猎物系统的动力学。在一定的假设下，通过分析特征值的分布，得到正稳态的稳定性和局部Hopf分岔的存在。此外，利用Wu的全局Hopf分岔结果，建立了正周期解的全局存在性。最后，通过一个例子和一些数值模拟来说明理论结果。