title: 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.
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.
authors.forename: Zhongkui
authors.initials: Z
authors.lastname: Sun
authors.affiliation: College of Mathematics and Information Science, Shaan'xi Normal University, Xi'an 710062, People's Republic of China.
authors.forename: Xiaoli
authors.initials: X
authors.lastname: Yang
authors.affiliation: Department of Mathematics and Information Science, Chang'an University, Xi'an 710086, People's Republic of China.
authors.forename: Yuzhu
authors.initials: Y
authors.lastname: Xiao
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.
authors.forename: Wei
authors.initials: W
authors.lastname: Xu