Modulating resonance behaviors by noise recycling in bistable systems with time delay

Abstract

In this paper, the impact of noise recycling on resonance behaviors is studied theoretically and numerically in a prototypical bistable system with delayed feedback. According to the interior cooperating and interacting activity of noise recycling, a theory has been proposed by reducing the non-Markovian problem into a two-state model, wherein both the master equation and the transition rates depend on not only the current state but also the earlier two states due to the recycling lag and the feedback delay. By virtue of this theory, the formulae of the power spectrum density and the linear response function have been found analytically. And the theoretical results are well verified by numerical simulations. It has been demonstrated that both the recycling lag and the feedback delay play a crucial role in the resonance behaviors. In addition, the results also suggest an alternative scheme to modulate or control the coherence or stochastic resonance in bistable systems with time delay.

Delay-induced stochastic bifurcations in a bistable system under white noise

“…It has been reported that time delay may induce the complex dynamics in dynamical systems. [8][9][10][11][12][13][14][15][16][17][18][24][25][26][27][28] In this part, the effect of time delay on bifurcation's behavior has been investigated in system (1) together with Gaussian white noise, as Fig. 4 displays.…”

“…Up to now, analytical researches have been concerned with the stability and performance in nonlinear stochastic DDSs, 19 the approximate solutions in nonlinear stochastic systems with small delays, [20][21][22][23] and the dynamical behaviors including resonance and bifurcations. [24][25][26][27][28] Besides, stochastic DDSs are widely used in other fields. For instance, Frank and Beek 29 were dedicated on exploring the biological systems, with the adoption of linear stochastic delay differential equations.…”