Stochastic resonance in the presence of slowly varying control parameters

Nicolis, C.; Nicolis, Grégoire

doi:10.1088/1367-2630/7/1/008

Cited by 13 publications

(13 citation statements)

References 12 publications

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“…4: the standard Gaussian and the Lévy distribution. The assumption of a Gaussian is consistent with previous work [18,26,27,30] and follows the typical assumptions in the literature: zero mean and correlation ξ(t), ξ(t ′ ) = σ 2 dtδ(t − t ′ ). The Lévy noise term is, on the other hand, less common.…”

Section: The Effect Of Noise Model On Branch Selectivitysupporting

confidence: 73%

“…A typical bifurcation representing decision-making in biology [10,11] or second-order phase transitions in physical systems [13,[26][27][28][29][30] is that underlying Eq. (1).…”

Section: A Forward Bifurcationsmentioning

confidence: 99%

“…Nevertheless, there are two fundamental components at play. First, the escape rate diminishes as λ reaches higher values, especially from x + to x − ; this arises from the difference between the potential associated with x +,− and x u becoming larger as λ is swept [30]. Therefore, the potential difference traps the system in x + due to g. On another side, if the simulations are long enough, the chances of converging towards the positive branch are higher due to the positive heavy-tailed Lévy noise term.…”

Section: The Effect Of Noise Model On Branch Selectivitymentioning

confidence: 99%

“…3 (a)). Moreover, the nature of signals and networks in biology dictates that the drivers are often compounded [30] and stochastic [4]. A forward-reverse simulation experiment stands, therefore, as a closer representation of the dynamical behaviour of the typical circuitry determining cellular decision making.…”

Section: B Forward-reverse Bifurcationsmentioning

confidence: 99%

See 3 more Smart Citations

Sensitivity of asymmetric rate-dependent critical systems to initial conditions: Insights into cellular decision making

Nené¹,

Rivington²,

Zaikin³

2018

Phys. Rev. E

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The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision making in biological systems. We achieve this by extending previous studies that resorted to simple bifurcation normal forms, although in the present case we focus primarily on the issue of the system's sensitivity to initial conditions in the presence of two different noise distributions, Gaussian and Lévy. In addition, we also assess the impact of two-way sweeping at different rates through the critical region of a canonical Pitchfork bifurcation with a constant external asymmetry. The parallel with decision making in biocircuits is performed on this simple system since it is equivalent in its available states and dynamics to more complex genetic circuits published previously. Overall we verify that rate-dependent effects, previously reported as being important features of bifurcating systems, are specific to particular initial conditions. Processing of each starting state, which for the normal form underlying this study is akin to a classification task, is affected by the balance between sweeping speed through critical regions and the type of fluctuations added. For the heavy-tailed noise, two-way dynamic bifurcations are more efficient in processing the external signals, here understood to be jointly represented by the critical parameter profile and the external asymmetry amplitude, when compared to the system relying on escape dynamics. This is particular to the case when the system starts at an attractor not favored by the asymmetry and, in conjunction, when the sweeping amplitude is large.

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Section: The Effect Of Noise Model On Branch Selectivitysupporting

confidence: 73%

“…A typical bifurcation representing decision-making in biology [10,11] or second-order phase transitions in physical systems [13,[26][27][28][29][30] is that underlying Eq. (1).…”

Section: A Forward Bifurcationsmentioning

confidence: 99%

Section: The Effect Of Noise Model On Branch Selectivitymentioning

confidence: 99%

Section: B Forward-reverse Bifurcationsmentioning

confidence: 99%

See 2 more Smart Citations

Sensitivity of asymmetric rate-dependent critical systems to initial conditions: Insights into cellular decision making

Nené¹,

Rivington²,

Zaikin³

2018

Phys. Rev. E

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show abstract

“…Collins et al introduced a multiplicative aperiodic signal into a symmetric bistable potential with the presence of additive noise, and found aperiodic stochastic resonance [23]. Recently, Nicolis and Nicolis studied the stochastic resonance in the presence of slowly varying control parameters and a multiplicative periodic signal in a bistable system [24]. Their results may give rise to a new method for the control of the transition rates [25].…”

Section: Introductionmentioning

confidence: 99%

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Bai¹,

Du²,

Mei³

2009

Open Physics

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Abstract:The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth. PACS

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Delay induced steady-state transition and stochastic resonance for an ecological vegetation growth system subjected to multiplicative and additive noises

Wang

et al. 2018

Chinese Journal of Physics

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Stochastic resonance in the presence of slowly varying control parameters

Cited by 13 publications

References 12 publications

Sensitivity of asymmetric rate-dependent critical systems to initial conditions: Insights into cellular decision making

Sensitivity of asymmetric rate-dependent critical systems to initial conditions: Insights into cellular decision making

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Delay induced steady-state transition and stochastic resonance for an ecological vegetation growth system subjected to multiplicative and additive noises

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