Vibrational resonance in a time-delayed genetic toggle switch

Daza, Álvar; Wagemakers, Alexandre; Rajasekar, S.; Sanjuán, Miguel A. F.

doi:10.1016/j.cnsns.2012.07.010

Cited by 51 publications

(31 citation statements)

References 26 publications

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“…In systems with linear damping, VR has already been widely investigated [38][39][40][41][42][43][44][45] following an early study by Landa and McClintock [36]. The results have shed light on the contributions to the effective potential of the various components of the high frequency signal [27], as well as the roles played by system parameters such as delay and fractional order terms in the induction, enhancement and control of VR [46][47][48][48][49][50][51]. However, relatively little attention has been paid to the possible contribution of nonlinear dissipation to the occurrence of VR, as described very recently for a prestressed beam fixed at both ends [52] and for a biharmonically driven plasma [53].…”

Section: Introductionmentioning

confidence: 99%

Vibrational resonance in an inhomogeneous medium with periodic dissipation

et al. 2017

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The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

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Section: Introductionmentioning

confidence: 99%

Vibrational resonance in an inhomogeneous medium with periodic dissipation

et al. 2017

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“…In this case we apply SAM to the ODE system in (9) in the interval 0 ≤ t ≤ M T with M = τ /T (see Figure 1). In the short final interval M T ≤ t ≤ τ (whose length is < T ) we integrate numerically the oscillatory problem itself and for this purpose we choose the integrator and step length being used for the microintegrations.…”

Section: Case Ii: the Delay Is Not An Integer Multiple Of The Periodmentioning

confidence: 99%

“…In the absence of external slow and fast forcing (A = B = 0) the system represents a delayed genetic toggle switch, a synthetic gene regulatory network [14]. The paper [9] studies the phenomenon of vibrational resonance [17,19] of the switch, i.e. the enhancement of the response to the slow forcing created by the presence of the high frequency forcing.…”

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confidence: 99%

High-order stroboscopic averaging methods for highly oscillatory delay problems

Calvo

Sanz‐Serna

Zhu

2020

Applied Numerical Mathematics

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We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant delays. The methodology suggested provides algorithms of arbitrarily high accuracy.Mathematical Subject Classification (2010) 65L03, 34C29 Keywords Delay differential equations, stroboscopic averaging, highly oscillatory problems IntroductionThis paper suggests and analyzes heterogeneous multiscale methods [10,11,13,12,18,1,23,5] for the numerical solution of highly oscillatory systems of delay differential equations (DDEs) with constant delays. The methods may achieve arbitrarily high orders of convergence and are based on the idea of the stroboscopic averaging method (SAM) [3,4] for highly oscillatory ordinary differential equations (ODEs).

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“…When there is no forcing (A = B = 0), the system represents a delayed genetic toggle switch, a synthetic gene regulatory network [12]. The forced system was studied in [11] as an instance of the emergence of vibrational resonance [13,15], i.e. the enhancement, due to the presence of the fast forcing, of the response of the system to the slow forcing.…”

Section: An Examplementioning

confidence: 99%

Word series high-order averaging of highly oscillatory differential equations with delay

Sanz‐Serna

Zhu

2019

Applied Mathematics and Nonlinear Sciences

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We show that, for appropriate combinations of the values of the delay and the forcing frequency, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word-series techniques to obtain high-order averaged equations for differential equations without delay.Mathematical Subject Classification (2010) 34C29

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Vibrational resonance in a time-delayed genetic toggle switch

Cited by 51 publications

References 26 publications

Vibrational resonance in an inhomogeneous medium with periodic dissipation

Vibrational resonance in an inhomogeneous medium with periodic dissipation

High-order stroboscopic averaging methods for highly oscillatory delay problems

Word series high-order averaging of highly oscillatory differential equations with delay

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