In this paper, we propose and study the dynamics of a non-autonomous biocontrol model concerned with native consumer $A$, biocontrol agent $B$ and their common predator $L$. We assume that some parameters in our proposed model are nonnegative functions instead of being bounded below by positive reals. This assumption is more realistic but makes mathematical proofs more challenging. We first study the positive invariance, permanence, and the global attractivity of bounded positive solution and boundary solution of the proposed model with general time-dependent parameters. Then we focus on the dynamics of the model with periodic parameters which include the existence and uniqueness of positive periodic solutions, and the global asymptotic stability of boundary periodic solution. We also explore and discuss the effects of introducing the biocontrol agent to ecosystem through theoretical analysis and numerical simulations. Our results show that introducing the biocontrol agent to ecosystem has positive effects by promoting its biodiversity and coexistence of all species, also potentially has negative effects by eliminating the predator. In addition, our numerical simulations show that (i) the amplitudes of periodic parameters could affect the permanence of non-autonomous periodic system; and (ii) the non-autonomous periodic system may suppress or improve the permanence of its autonomous version but related to the amplitudes of periodic parameters.

在本文中，我们提出并研究了与本地消费者有关的非自治生物控制模型的动力学 $\mathrm{一种}$，生物防治剂 $乙$ 和他们共同的掠食者 $\mathrm{大号}$。我们假设我们提出的模型中的某些参数是非负函数，而不是受到正实数的限制。这种假设更现实，但使数学证明更具挑战性。我们首先研究带有一般时间相关参数的模型的有界正解和边界解的正不变性，持久性和全局吸引性。然后，我们关注具有周期参数的模型动力学，其中包括正周期解的存在性和唯一性，以及边界周期解的全局渐近稳定性。我们还通过理论分析和数值模拟来探讨和讨论将生物防治剂引入生态系统的效果。我们的结果表明，将生物防治剂引入生态系统可通过促进其生物多样性和所有物种的共存而产生积极作用，而消除捕食者也可能具有负面影响。此外，我们的数值模拟结果表明：（i）周期性参数的幅度可能会影响非自治周期性系统的持久性；（ii）非自治周期系统可以抑制或改善其自治版本的永久性，但与周期参数的幅度有关。