Vibrational resonance analysis in a gene transcriptional regulatory system with two different forms of time-delays

Abstract

The impacts of two different forms of time-delays on vibrational resonance are explored in a gene regulatory model excited by both a low-frequency force and a high-frequency force. The response amplitude Q is obtained numerically to quantify the occurrence of vibrational resonance. Through finding, the vibrational resonance can be enhanced by a linear time-delay that can arise in the degradation process, while the nonlinear time-delay occurring in the synthesis process can weaken the resonance phenomenon, which is different from the role of linear time-delay. And both of the above delays can induce changes in the number of resonances. Thus, the optimum vibrational resonance can be achieved and useful genetic information can be easily acquired by controlling the time-delay. Furthermore, it is interesting to note that the resonance is always present and the effects of the time-delays are still valid when a square-wave signal is used to replace the cosine signal.