In this paper, we study the bifurcation of periodic solutions for a four-dimensional deployable circular mesh antenna system. The tools for proving these results are the averaging theory and Brouwer degree theory. Based on constructing displacement maps, we study the bifurcation of the periodic solutions of linear center, and to discuss the maximum number of periodic solutions in certain parameter control conditions. The results in this paper are helpful to the study of nonlinear dynamic characteristics and vibration control of deployable circular mesh antenna model.

中文翻译：

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1:2内谐振圆网状天线系统中周期解的分岔及其最大数

在本文中，我们研究了四维可展开圆形网状天线系统的周期解的分岔。证明这些结果的工具是平均理论和 Brouwer 度理论。在构造位移图的基础上，研究了线性中心周期解的分岔问题，并讨论了在一定参数控制条件下的最大周期解数。本文的研究结果有助于研究可展开圆形网状天线模型的非线性动力学特性和振动控制。