Nonlinear Dynamics

, Volume 92, Issue 2, pp 511–529 | Cite as

Noise-induced phenomena in a versatile class of prototype dynamical system with time delay

  • Tao Yang
  • Qingjie Cao
Original Paper


This work presents a general class of prototype birhythmic dynamical systems, which can be extensively used to study the generation of complex bifurcation of limit cycles. Using a delay nonlinear Langevin approach, the stationary probability distribution and the escape problem are investigated under the influences of noise and time delay feedback. We discuss a new mechanism for the translocation of the amplitude in which the energy originates from noise. The results indicate that depending on the parameter space the system exhibits a transition from birhythmic to monorhythmic behavior or amplitude death. Besides, results demonstrated that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic bifurcation. Moreover, a novel finding is that the mean first passage time non-monotonically depends on the noise intensity and the dominant frequency of the oscillation. This finding represents the evidence of the noise-enhanced stability and stochastic resonant activation in the prototype dynamical system, whose occurrence is maintained for different values of the delay feedback intensity.


Stochastic processes Time delay Noise-enhanced stability Stochastic resonant activation 



The authors would like to acknowledge the financial support from the Natural Science Foundation of China (Grant Nos. 11572096, 11665014 and 11732006) and the authors also wish to express their appreciation to the anonymous reviewers for their insightful reading and helpful comments.


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Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinPeople’s Republic of China

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