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Effects of Combined Feedbacks and Recycling Noise on a Birhythmic Self-sustained Oscillator

Abstract

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.

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Correspondence to A. Chéagé Chamgoué.

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Chamgoué, A.C., Ndemanou, B.P., Yamapi, R. et al. Effects of Combined Feedbacks and Recycling Noise on a Birhythmic Self-sustained Oscillator. Braz J Phys 51, 376–385 (2021). https://doi.org/10.1007/s13538-020-00832-0

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Keywords

  • van der Pol oscillator
  • Birhythmicity
  • Hopf bifurcation
  • Time-delay feedback
  • Recycling noise
  • Stochastic averaging method
  • P-Bifurcation