中文摘要：

与ENSO相关的热带大尺度海-气相互作用是影响全球气候年际变化的主要过程之一.该文从一个海-气相互作用方程组出发,推广了一个具有一般形式的海-气耦合气候系统非线性扰动模式.运用拓扑度理论,从数学上严格证明了一定条件下该模式存在周期正解的结果,并分析了所得结果潜在的应用价值.海-气相互作用研究,有助于理解气候变化过程,为气候模拟和预报提供理论基础.

英文摘要：

The focus was given on the tropical large-scale ocean-atmosphere interaction associated with ENSO,which was considered as one of the most important mechanisms for the global inter-annual climate variability. From a group of sea-air coupling equations,a nonlinear disturbed model was built for sea-air coupling climate systems. Based on the continuation theorem of Mawhin＇s coincidence degree,the existence of positive periodic solutions to a class of nonlinear problems was discussed. A strict proof of the existence of positive periodic solutions to the model was obtained,and the potential application value of the result was expected. The study of air-sea interaction,which helps to understand the process of climate variability,provides a theoretical basis for climate simulation and prediction.