In this paper we study the spruce-budworm interaction model with Holling's type II functional response. The existence, number and stability of equilibria are studied. Moreover, we prove the existence of relaxation oscillations by using singular perturbation method and give an asymptotic expression of the period of relaxation oscillations. Finally, the parameter ranges which allow the relaxation oscillations in several scenarios are explored and displayed by conducting numerical simulations.

中文翻译：

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具有Holling II型功能性反应的云杉-bud虫相互作用模型中的弛豫振荡

在本文中，我们研究了具有Holling II型功能性反应的云杉-天虫相互作用模型。研究了均衡的存在，数量和稳定性。此外，我们通过奇异摄动法证明了弛豫振荡的存在，并给出了弛豫振荡周期的渐近表达。最后，通过进行数值模拟，探索并显示了在几种情况下允许弛豫振荡的参数范围。