中文摘要：

基于经典的间隙单齿轮副非线性动力学模型,采用伪不动点追踪法研究了齿轮系统共存的周期解,采用胞映射方法研究了各共存周期解的全局稳定性。结果发现,在考查参数下,齿轮系统存在3种不同形怎的周期运动,即分别是周期1解（0.634 6,0.062 5）、周期2解（-0.141 4,-0.150 5）和周期4解（-0.2053,-0.151 8）。其中,周期1解不具备长期运动稳定性;周期2解的吸引域面积较大且连续,具有较高的局部稳定性;周期4解的吸引域不连续,运动的初值稳定性较差。

英文摘要：

The coexisting periodic solutions and their global stability of a nonlinear gear system are studied in this paper.Based on the classical nonlinear gear dynamic model,quasi-fixed-point tracing method is used to study the coexisting periodic solutions and cell-to-cell mapping method is used to study the global attracting domain of every coexisting periodic solution.The results reveal that the gear system has 3 coexisting periodic solutions,comong which which period-1 solution（0.634 6,0.062 5） doesn’t have long-term moment stability,period-2 solution（-0.141 4,-0.150 5） has a good local stability,and period-4 solution（-0.205 3,-0.151 8） has a poor local stability.