Multiplicative stochastic resonance

Gammaitoni, L.; Marchesoni, F.; Menichellasaetta, E.; Santucci, S.

doi:10.1103/physreve.49.4878

Cited by 94 publications

(48 citation statements)

References 23 publications

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“…when the potential modulation period is twice the mean residence time of the noise-driven particle. Experimental works on stochastic resonance are almost exclusively using amplitude modulation going along with additive amplitude noise or multiplicative amplitude noise [10,20,37,44,45]. In this case, it corresponds to a pure one dimensional effect.…”

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confidence: 99%

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane

et al. 2017

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Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced nano-electromechanical membrane by evidencing the enhancement of a weak phase modulated signal thanks to the addition of phase noise. Based on a general forced Duffing oscillator model, we demonstrate experimentally and theoretically that phase noise acts multiplicatively inducing important physical consequences. These results may open interesting prospects for phase noise metrology or coherent signal transmission applications in nanomechanical oscillators. Moreover, our approach, due to its general character, may apply to various systems.Stochastic resonance whereby a small signal gets amplified resonantly by application of external noise has been introduced originally in paleoclimatology [1,19] to explain the recurrence of ice ages and has then been observed in many other areas including neurobiology [6,16] [3,33,34,42]. Implementation of stochastic resonances involves generally three ingredients : (i) the existence of metastable states separated by an activation energy, as in excitable or bistable nonlinear systems, (ii) a coherent excitation, whose amplitude is however too weak to induce deterministic hopping between the states, and (iii) stochastic processes inducing random jumps over the potential barrier. In the classical picture of a bistable system, this corresponds to the motion of a fictive particle in a double-well potential periodically modulated in amplitude by the signal and subjected to noise [21]. When an optimal level of noise is reached, the system's response power spectrum displays a peak in the signal to noise ratio, unveiling the stochastic resonance phenomenon. The resonance occurs as a 'bona-fide' resonance in a frequency band around a signal frequency approximately given by the time-matching condition [5,22], i.e. when the potential modulation period is twice the mean residence time of the noise-driven particle. Experimental works on stochastic resonance are almost exclusively using amplitude modulation going along with additive amplitude noise or multiplicative amplitude noise [10,20,37,44,45]. In this case, it corresponds to a pure one dimensional effect. Few studies take advantage of a bidimensional phase space by e.g. using phase modulation and/or phase noise (i.e. phase random fluctuations of input signal) [15,23]. Most of them use amplitude noise to demonstrate amplitude stochastic resonance, or introduce noise in the form of the response of a stochastic oscillator [39]. However in the latter scheme, neither the noise nor the modulation are controlled, thus preventing to unveil the specific roles of phase modulation and phase noise in stochastic resonance.In this Letter, stochastic resonance is implemented in a nonlinear nanomechanical oscillator forced close to its resonant frequency. It enables, in a bidimensionnal phase space, the implementation of phase...

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confidence: 99%

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane

et al. 2017

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“…It is originally proposed for symmetrical bistable systems with additive noise source [12]. The improvements of the theory of SR have included monostable systems [13,14], asymmetrical systems [15] and double-noises systems [16][17], but in all these studies the system has an additive noise source and an independent external field. To pure multiplicative noise systems, especially to many complex dynamical systems, it is still far difficult to solve them exactly, thus numerical methods are comparatively convenient options to solve these complex dynamical systems [18,19].…”

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Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability

2006

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The effects of pure multiplicative noise on stochastic resonance in an anti-tumor system modulated by a seasonal external field are investigated by using theoretical analyses of the generalized potential and numerical simulations. For optimally selected values of the multiplicative noise intensity quasisymmetry of two potential minima and stochastic resonance are observed. Theoretical results and numerical simulations are in good quantitative agreement. Chemotherapy remains a traditional option for most advanced cancer. Immunotherapy, however, is a less conventional treatment modality. Usually, chemotherapy and immunotherapy have been regarded as unrelated, so relatively little research has investigated the relationship between these two therapies. Chemotherapy kills tumor cells in a special way periodically, but immunotherapy restrains the growth of tumor cells in a more likely linear way [1,2]. Since these different responses of tumor cells to chemotherapy and immunotherapy, when taken together, they imply that there is an interesting and significative case for combining chemotherapy and immunotherapy in tumor treatment.More than ever, cancer research is now an interdisciplinary effort which requires a basic knowledge of commonly used terms, facts, issues, and concepts. In the past decade, many studies have focused on the growth law of tumor cells via dynamics approach, specially using noise dynamics [3][4][5][6][7][8][9]. Phase transition of tumor growth induced by noises is one of the most novel foundations in recent years. Another phenomenon-known as stochastic resonance (SR) -shows that adding noise to a system can sometimes improve its ability to transfer information. The basic three ingredients of stochastic resonance are a threshold, a noise source and a weak input, it is clear that stochastic resonance is a common case and generic enough to be observable in a large variety of nonlinear dynamical systems [10,11]. Thus, it is reasonable to believe that SR can also occur in a tumor dynamical system.The mean field approximate analysis is a conventional theory for SR. It is originally proposed for symmetrical bistable systems with additive noise source [12]. The improvements of the theory of SR have included monostable systems [13,14], asymmetrical systems [15] and double-noises systems [16][17], but in all these studies the system has an additive noise source and an independent external field. To pure multiplicative noise systems, especially to many complex dynamical systems, it is still far difficult to solve them exactly, thus numerical methods are comparatively convenient options to solve these complex dynamical systems [18,19].In this letter, chemotherapy and immunotherapy are joined by an anti-tumor model with three elements, which are (1) a fluctuation of growth rate, (2) an immune form, and (3) a weak seasonal modulability induced by chemotherapy. Based on the analyses on its unique stochastic differential equation and relevant Fokker-Planck equation, we investigate a new type of SR phenomenon of an...

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“…[24]. The multiplicative SR is of interest since multiplicative noise usually responds for the fluctuating control parameters [25].…”

Section: The Effects Of Time Delay On the Stochastic Resonance Of Thementioning

confidence: 99%

The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

Du¹,

Mei²

2010

Physics Letters A

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Multiplicative stochastic resonance

Cited by 94 publications

References 23 publications

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane

Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability

The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

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