Stochastic resonance in multistable systems: The role of dimensionality

Nicolis, C.

doi:10.1103/physreve.86.011133

Cited by 23 publications

(14 citation statements)

References 15 publications

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“…We set out to obtain a pair of integro-differential equations which describes the equations of slow oscillations and the fast vibrations. The superposition of their solutions completely solves the PDM system given by in equation (22). Therefore we assume x y z.…”

Section: Theoretical Analysismentioning

confidence: 99%

“…The occurrence of multiple attractors is often determined by the system class such as dissipation strength, coupling type and intensity, time delay, amplitude and frequency of parameter perturbation, nature of external forcing and noise intensity [17,19]. These system components have been shown to influence several nonlinear phenomena observed in multistable systems including synchronization, memory capability mechanism in artificial neural networks, absolute negative mobility and current reversal, hidden and selfexcited attractors, chaos and nonlinear resonance [20][21][22][23][24]. A much studied type of nonlinear resonance observed in multistable systems with weak signal generated by applying white noise to an external signal with a broad frequency range is the stochastic resonance (SR) [25].…”

Section: Introductionmentioning

confidence: 99%

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Vibrational resonance in a multistable system with position-dependent mass

Roy-Layinde,

Omoteso,

Kolebaje

et al. 2023

Commun. Theor. Phys.

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The occurrence of vibrational resonance (VR) in a dual-frequency-driven multistable system with a spatially varying mass modelling particle with position-dependent mass (PDM) and evolving in a one-dimensional symmetric periodic potential has been investigated and reported in this paper. We numerically computed and analyzed the response amplitude, the effects of the PDM parameters ($m_0,a$) on the potential structure, the occurrence of VR and the bifurcation of the equilibrium points. It is shown that the PDM parameters, besides controlling VR, can induce unconventional resonance patterns through the variation of the potential well depth. The resonant states can be influenced through the cooperation of the PDM parameters and the external forcing leading the system from multiresonance state into single and double resonance states. The contributions of the fixed rest mass $m_0$ on the VR and the PDM-induced resonance are determined by threshold conditions imposed by the magnitude of the mass nonlinear strength $a$.

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Section: Theoretical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibrational resonance in a multistable system with position-dependent mass

Roy-Layinde,

Omoteso,

Kolebaje

et al. 2023

Commun. Theor. Phys.

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“…We shall argue in this and the following sections that the higher catastrophe that organizes the BH trimer dynamics is in fact the high order umbilic catastrophe known by its group-theoretic symbol, X 9 . This complicated object has previously been the subject of detailed theoretical analysis by Borghi [186] and by Berry and Howls [187], and plays an important role in optical refraction through twodimensional surfaces, such as water droplets [188], glass junctions [189], gravitational lensing [92], and has also been discussed in the context of stochastic resonance in two dimensions [190]. X 9 acts as an organizing centre for a multitude of lower catastrophes and we refer the reader to Fig.…”

Section: The X9 Catastrophementioning

confidence: 99%

Caustics in quantum many-body dynamics

Kirkby,

Yee,

Shi

et al. 2021

Preprint

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Caustics are a striking phenomena in natural optics and hydrodynamics: high-amplitude characteristic patterns that are singular in the short wavelength limit. We use exact numerical and approximate semiclassical analytic methods to study quantum versions of caustics that form in Fock space during far-from-equilibrium dynamics following a quench in the Bose Hubbard dimer and trimer models. Due to interparticle interactions, both models are nonlinear and the trimer is also nonintegrable. The caustics exhibit a hierarchy of morphologies described by catastrophe theory that are stable against perturbations and hence occur generically. The dimer case gives rise to discretized versions of folds and cusps which are the simplest two of Thom's catastrophes. The extra dimension available in the trimer case allows for higher catastrophes including the codimension-3 hyperbolic umbilic and elliptic umbilic catastrophes which we argue are organized by, and projections of, an 8-dimensional corank-2 catastrophe known as X9. These results indicate a hitherto unrecognized form of universality in quantum many-body dynamics organized by singularities.

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“…At present, most research achievements of stochastic resonance were based on the one-dimensional potential system, while the two-dimensional potential system lacks sufficient research due to the coupling of system state variables and the complexity of inter-well transitions. Nicolis (2012) and Nicolis and Nicolis (2017) extended the inter-well dynamics of a multi-stable system to a two-dimensional space and found that the synergistic effect of intermediate steady-state and multidimensional characteristics would enhance the system response. Therefore, the SR mechanism of the one-dimensional and two-dimensional potential systems is very worthy of attention and research.…”

Section: Introductionmentioning

confidence: 99%

Research and application of tristable stochastic resonance based on harmonic and pinning potential model

Liu

Zhang

2022

Journal of Vibration and Control

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In view of the unique potential barrier and complex potential function of the pining model, as well as the lack of researches on two-dimensional stochastic resonance, two new potential tristable models are proposed: one-dimensional tristable model and two-dimensional tristable model. The stochastic resonance mechanism and application of two potential systems under Gaussian white noise and weak external driving force are discussed and the differences and advantages of the two systems are analyzed in detail for the first time. First, the potential function and mean first passage time are analyzed. Second, according to the linear response theory, the probability flow method is used to calculate the spectral amplification. The effects of system parameters on spectral amplification of the two models are studied, and the two models are compared. Finally, the two models are applied to the detection of actual bearing fault signals together with the classical tristable system and the performance is compared. Both algorithms can detect fault signals effectively, but the two-dimensional model has better amplitude and difference, and the one-dimensional model has less interference burrs. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.

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Stochastic resonance in multistable systems: The role of dimensionality

Cited by 23 publications

References 15 publications

Vibrational resonance in a multistable system with position-dependent mass

Vibrational resonance in a multistable system with position-dependent mass

Caustics in quantum many-body dynamics

Research and application of tristable stochastic resonance based on harmonic and pinning potential model

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