Numerous studies have demonstrated the important role of noise in the dynamical behavior of a complex system. This work is devoted to investigating the constructive role of combined feedbacks and recycling random excitation on stochastic bifurcations and its regularization in a birhythmic oscillator. This possesses a bistability mode with the coexistence of two stable limit cycles in the deterministic case. However, so far, these combining effects on the birhythmic dynamic system have not been reported. Relying on the approximate methods, the harmonic approximation is adopted to drive the delay self-control feedback to state variables without delay noise. The dynamical behavior of the model is analyzed analytically using Hopf bifurcation theorem and numerically such as two-dimensional bifurcation diagrams with respect to two feedback parameters are obtained. Then, Fokker–Planck–Kolmogorov (FPK) equation and stationary probability density function (PDF) for amplitude are obtained by applying the stochastic averaging method. Based on these results, the influence of related parameters of recycling noise and damping coefficient on the stochastic P-bifurcation is studied.

大量研究表明，噪声在复杂系统的动力学行为中起着重要作用。这项工作致力于调查组合反馈和随机激发对随机分叉及其在双节律振荡器中的正则化的建设性作用。在确定性情况下，它具有双稳态模式和两个稳定极限环并存。然而，到目前为止，尚未报道这些对节律动力学系统的联合作用。依靠近似方法，采用谐波近似将延迟自控制反馈驱动为无延迟噪声的状态变量。使用Hopf分支定理对模型的动力学行为进行分析，并在数值上获得关于两个反馈参数的二维分支图。然后，采用随机平均方法，获得了Fokker-Planck-Kolmogorov（FPK）方程和振幅的平稳概率密度函数（PDF）。基于这些结果，研究了循环噪声和阻尼系数的相关参数对随机P-分支的影响。