外来物种入侵作为自然界中一种常见的生物现象，严重影响着生物多样性和生态平衡，对全球经济造成了巨大的损失。研究入侵现象是一项非常有意义的课题，它为预测和控制入侵物种的扩张提供了理论基础。本项目旨在研究非齐次时间周期环境下种群入侵模型的动力学，该类模型是由带有自由边界的反应扩散方程来描述的。针对单种群模型和两种群竞争模型，分别在不加对流项和加入对流项两种情形下给出内禀增长率变号时初始值、对流系数以及边界条件对种群扩张与灭绝的影响，确定对流系数的最优控制条件，并通过数值模拟验证理论结果的正确性。

As a common biological phenomenon in nature, alien species invasion seriously affects the biodiversity and ecological balance, and makes a great loss to the global economy. The study of invasion is a very meaningful topic, and it provides a theoretical basis for the prediction and control of the spreading of invasive species. The purpose of this project is to study the dynamics of species invasion models in heterogeneous time-periodic environment, which are described by the reaction-diffusion equations with free boundaries. For single-species models and two-species competition models both with and without convection terms, we establish the influences of initial data, convection coefficients and boundary conditions in spreading and vanishing of species when the intrinsic growth rates change signs, determine the optimal control conditions of convection coefficients, and verify the correctness of the obtained theoretical results by numerical simulation.