中文摘要：

由于空间等离子体间接观察的不确定性和不可重复性以及只能进行被动实验的局限性，为了准确地描述空间等离子体粒子运动的动力学特征．建立了一类太空等离子体单粒子运动的非线性模型．首先运用重合度理论探讨了一类非线性问题的周期解，然后将其应用于太空等离子体单粒子运动模型的同宿轨问题的研究，获得了该模型存在同宿轨的新结果，为研究空间环境提供了更好的观测和理论基础．

英文摘要：

Due to uncertainty and non-repeatability in the indirect observation of space plasma, and limitation of the passive experiment, in order to describe the dynamic characteristics of the space plasma particle motion accurately, a nonlinear motion model of a single space plasma particle was proposed. By dint of Mawhin＇ s continuation theorem, the existence of periodic so- lutions to a class of nonlinear problems was discussed, and in turn, the homoclinic orbit of the motion model for a single space plasma particle was investigated. A new result about the exist- ence of the homoclinic orbit was obtained. The result provides a better basis for observation and theoretical study in space environment.