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

作者：Yang, Tao; Cao, Qingjie^*

来源：Nonlinear Dynamics, 2018, 92(2): 511-529.

DOI：10.1007/s11071-018-4072-x

• Stochastic processes
• Time delay
• Noise-enhanced stability
• Stochastic resonant activation

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.

• 出版日期2018-4
• 单位哈尔滨工业大学