The transition of gene switch induced by external noises (multiplicative external noise and additive external noise) and external signals is investigated in the genetic regulatory system. Results show that the state-to-state transition of gene switch as well as resonant behaviors, such as the explicit coherence resonance (ECR), implicit coherence resonance (ICR) and control parameter coherence biresonance (CPCBR), can appear when noises are injected into the genetic regulatory system. The ECR is increased with the increase of the control parameter value when starting from the supercritical Hopf bifurcation parameter point, and there exists a critical control parameter value for the occurrence of ECR. However, the ICR is decreased as the control parameter value is increased when starting from the subcritical Hopf bifurcation point. In particular, the coherence of ECR is higher and more sensitive to noise than that of ICR. When an external signal is introduced into the system, the enhancement or suppression of the CPCBR and the number of peaks strongly depend on the frequency and amplitude of the external signal. Furthermore, the gene regulation system can selectively enhance or decrease the noise-induced oscillation signals at preferred frequency and amplitude of an external signal.

中文翻译：

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遗传调控系统中基因开关和相干共振的外部噪声和外部信号诱导的转变

在遗传调控系统中研究了由外部噪声（乘性外部噪声和加性外部噪声）和外部信号引起的基因开关的转变。结果表明，当注入噪声时，会出现基因开关的状态到状态转换以及共振行为，例如显式相干共振 (ECR)、隐式相干共振 (ICR) 和控制参数相干双共振 (CPCBR)进入基因调控系统。从超临界Hopf分岔参数点出发，ECR随着控制参数值的增大而增大，存在ECR发生的临界控制参数值。然而，当从亚临界 Hopf 分叉点开始时，ICR 随着控制参数值的增加而降低。特别是，ECR 的相干性比 ICR 更高，对噪声更敏感。当外部信号引入系统时，CPCBR 的增强或抑制以及峰值的数量很大程度上取决于外部信号的频率和幅度。此外，基因调控系统可以在外部信号的优选频率和幅度下选择性地增强或降低噪声诱导的振荡信号。