We present the existence and uniqueness of random periodic path for stochastic dynamical systems generated by random switching stochastic differential equations (SDEs). These classes of SDEs arise as concrete models in molecular dynamics, biochemistry, climatology, wireless communications, financial mathematics, biological and artificial neural networks, etc. Random periodic processes are inevitable in these classes of stochastic dynamical systems due to the nonlinearity of their processing and the presence of time-dependent applied current. In our investigation, we employed Lyapunov second method and the theory of M-matrices, which are verifiable in terms of the coefficients of the SDE and the switching rates.

我们介绍了由随机切换随机微分方程 (SDE) 生成的随机动力系统的随机周期路径的存在性和唯一性。这些类别的 SDE 作为分子动力学、生物化学、气候学、无线通信、金融数学、生物和人工神经网络等领域的具体模型出现。随机周期过程在这些类别的随机动力系统中是不可避免的，因为它们的处理和处理具有非线性随时间变化的施加电流的存在。在我们的调查中，我们采用了 Lyapunov 第二种方法和 M 矩阵理论，它们可以根据 SDE 的系数和转换率进行验证。