In this paper, a parasitic-mutualistic model of mistletoes and birds defined in a heterogneous and periodically evolving domain is comprehensively investigated to reveal some new dynamical phenomena caused by the domain evolution. By establishing the core spatial-temporal risk index R₀^B and R₀^M for birds population and mistletoes-birds population, respectively, the fundamental extinction, persistence and coexistence behaviors are studied, and distinguished by such indexes. Moreover, the impact of domain evolution on the viability of mistletoes is examined as well, and it is concluded that the average expansion of the domain can enhance mistletoes’ transmission capability, therefore, pro-mote the viability of mistletoes, and vice versa. Finally, numerical simulations are also exhibited for some specific cases to verify the theoretical conclusions.

中文翻译：

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周期性进化域上槲寄生和鸟类的异质寄生-互生模型

在本文中，对定义在异质且周期性演化的域中的槲寄生和鸟类的寄生-相互模型进行了全面研究，以揭示由域演化引起的一些新的动力学现象。通过建立核心时空风险指数R ₀ ^B和R ₀ ^M对于鸟类种群和槲寄生鸟类种群，分别研究了它们的基本灭绝，持久性和共存行为，并通过这些指标进行区分。此外，还研究了域演化对槲寄生活力的影响，得出的结论是，域的平均扩展可以增强槲寄生的传递能力，从而促进了槲寄生的活力，反之亦然。最后，还针对某些特定情况进行了数值模拟，以验证理论结论。