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Li S, Wang Z, Yang J, Sanjuán MAF, Huang S, Lou L. Ultrasensitive vibrational resonance induced by small disturbances. CHAOS (WOODBURY, N.Y.) 2023; 33:123111. [PMID: 38055719 DOI: 10.1063/5.0172108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 11/14/2023] [Indexed: 12/08/2023]
Abstract
We have found two kinds of ultrasensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultrasensitive vibrational resonance is transient behavior caused by transient chaos. Considering a long-term response, the system will transform from transient chaos to a periodic response. The pattern of vibrational resonance will also transform from ultrasensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultrasensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultrasensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from ultrasensitive vibrational resonance to conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultrasensitive vibrational resonance appears and the plot of the response amplitude vs the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly periodic, it usually corresponds to the conventional vibrational resonance. The ultrasensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultrasensitive vibrational resonance as transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.
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Affiliation(s)
- Shangyuan Li
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Zhongqiu Wang
- School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Jianhua Yang
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Miguel A F Sanjuán
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Shengping Huang
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Litai Lou
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
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Vibrational Resonance and Electrical Activity Behavior of a Fractional-Order FitzHugh–Nagumo Neuron System. MATHEMATICS 2021. [DOI: 10.3390/math10010087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Making use of the numerical simulation method, the phenomenon of vibrational resonance and electrical activity behavior of a fractional-order FitzHugh–Nagumo neuron system excited by two-frequency periodic signals are investigated. Based on the definition and properties of the Caputo fractional derivative, the fractional L1 algorithm is applied to numerically simulate the phenomenon of vibrational resonance in the neuron system. Compared with the integer-order neuron model, the fractional-order neuron model can relax the requirement for the amplitude of the high-frequency signal and induce the phenomenon of vibrational resonance by selecting the appropriate fractional exponent. By introducing the time-delay feedback, it can be found that the vibrational resonance will occur with periods in the fractional-order neuron system, i.e., the amplitude of the low-frequency response periodically changes with the time-delay feedback. The weak low-frequency signal in the system can be significantly enhanced by selecting the appropriate time-delay parameter and the fractional exponent. In addition, the original integer-order model is extended to the fractional-order model, and the neuron system will exhibit rich dynamical behaviors, which provide a broader understanding of the neuron system.
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Omoteso KA, Roy-Layinde TO, Laoye JA, Vincent UE, McClintock PVE. Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator. ULTRASONICS SONOCHEMISTRY 2021; 70:105346. [PMID: 33011444 PMCID: PMC7786605 DOI: 10.1016/j.ultsonch.2020.105346] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Revised: 08/06/2020] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.
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Affiliation(s)
- K A Omoteso
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - U E Vincent
- Department of Physical Sciences, Redeemer's University, P.M.B. 230, Ede, Nigeria; Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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Pal K, Ray DS. Antiresonance and Stabilization in Spatio‐Temporal Dynamics of a Periodically Driven Gray‐Scott Reaction‐Diffusion System. ChemistrySelect 2020. [DOI: 10.1002/slct.202002810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Krishnendu Pal
- School of Chemical Sciences Indian Association for the Cultivation of Science Jadavpur, Kolkata 700032, West Bengal India
| | - Deb Shankar Ray
- School of Chemical Sciences Indian Association for the Cultivation of Science Jadavpur, Kolkata 700032, West Bengal India
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Wang KK, Wang YJ, Ye H, Li SH. Time delay and cross-correlated Gaussian noises-induced stochastic stability and regime shift between steady states for an insect outbreak system. INT J BIOMATH 2019. [DOI: 10.1142/s1793524519500487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
In this paper, we focus on investigating the stochastic stability and the regime transition between the endangered state and the boom state for a time-delayed insect growth system driven by correlated external and internal noises. By use of the Fokker–Planck equation, the method of small time delay approximation and the fast descent method, we explore in detail the joint action of noise terms and time delay on the mean reproduction and depression time for the insect population. Our investigations indicate that the pseudo-resonance phenomenon of the mean first-passage time (MFPT) occurs because of the impact of different noises and time delay. Through the numerical calculation, it is discovered that multiplicative noise can speed up the shift of the insect population from the boom state to the endangered one, while the noise correlation and time delay can propel the insect system to evolve from the endangered state to the boom state and improve the biological stability. In addition, the impact of the additive noise on the stability of the biological system depends on the positive and negative situation of the noise correlation. On the other hand, during the process of suppressing the insect explosion, it is beneficial to the pest control to amplify the association noise strength and weaken the intensities of the multiplicative, additive noises and time delay. However, during the process of eliminating the pests, it can produce nice effect on the disinsection to increase time delay, the intensities of multiplicative and additive noises and weaken the strength of noise correlation.
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Affiliation(s)
- Kang-Kang Wang
- School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, P. R. China
- Center of Complex Systems and Network Science Research, Southeast University, Nanjing 210096, P. R. China
| | - Ya-Jun Wang
- School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, P. R. China
| | - Hui Ye
- School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, P. R. China
| | - Sheng-Hong Li
- School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, P. R. China
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Sarkar P, Ray DS. Vibrational antiresonance in nonlinear coupled systems. Phys Rev E 2019; 99:052221. [PMID: 31212415 DOI: 10.1103/physreve.99.052221] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2019] [Indexed: 06/09/2023]
Abstract
We examine the response of a system of coupled nonlinear oscillators driven by a rapidly varying field, to a low frequency weak periodic excitation of one of the oscillators. The response amplitude of the weak field-driven oscillator at an optimal strength of the rapidly varying field exhibits a strong suppression accompanied by a large negative shift in its oscillation phase. The minimum can be identified as vibrational antiresonance in between the two maxima corresponding to vibrational resonance. This vibrational antiresonance can be observed only in nonlinear coupled systems and not in linearly coupled systems or in a single nonlinear oscillator, under similar physical condition. We discuss the underlying dynamical mechanism, the role of nonlinearity and high frequency in characterizing this counter-resonance effect. Our theoretical analysis is corroborated by detailed numerical simulations.
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Affiliation(s)
- Prasun Sarkar
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Roy-Layinde TO, Laoye JA, Popoola OO, Vincent UE, McClintock PVE. Vibrational resonance in an inhomogeneous medium with periodic dissipation. Phys Rev E 2017; 96:032209. [PMID: 29346993 DOI: 10.1103/physreve.96.032209] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Indexed: 06/07/2023]
Abstract
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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Affiliation(s)
- T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
| | - O O Popoola
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - U E Vincent
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
- Department of Physical Sciences, Redeemer's University, Ede, Nigeria
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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Roy-Layinde TO, Laoye JA, Popoola OO, Vincent UE. Analysis of vibrational resonance in bi-harmonically driven plasma. CHAOS (WOODBURY, N.Y.) 2016; 26:093117. [PMID: 27781458 DOI: 10.1063/1.4962403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven two-fluid plasma model with nonlinear dissipation. An equation for the slow oscillations of the system is analytically derived in terms of the parameters of the fast signal using the method of direct separation of motion. The presence of a high frequency externally applied electric field is found to significantly modify the system's dynamics, and consequently, induce VR. The origin of the VR in the plasma model has been identified, not only from the effective plasma potential but also from the contributions of the effective nonlinear dissipation. Beside several dynamical changes, including multiple symmetry-breaking bifurcations, attractor escapes, and reversed period-doubling bifurcations, numerical simulations also revealed the occurrence of single and double resonances induced by symmetry breaking bifurcations.
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Affiliation(s)
- T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
| | - O O Popoola
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - U E Vincent
- Department of Physical Sciences, Redeemers' University, Ede, Nigeria
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Chizhevsky VN. Noise-induced suppression of nonlinear distortions in a bistable system with biharmonic excitation in vibrational resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032902. [PMID: 26465535 DOI: 10.1103/physreve.92.032902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2015] [Indexed: 06/05/2023]
Abstract
This paper is a report of the experimental evidence of suppression of vibrational higher-order harmonics in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies in the phenomenon of vibrational resonance when an optimal amount of white, Gaussian noise is applied. A quantitative characterization of the suppression is given on the basis of the coefficient of nonlinear distortions. The behavior of the coefficient of nonlinear distortions is studied in wide ranges of the added noise intensity, the dc current, and the amplitude of the harmonic signals. The experimental results are compared with a numerical simulation of a Langevin model showing good agreement.
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Affiliation(s)
- V N Chizhevsky
- B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 220072 Minsk, Belarus
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Chizhevsky VN. Experimental evidence of vibrational resonance in a multistable system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062914. [PMID: 25019858 DOI: 10.1103/physreve.89.062914] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Indexed: 06/03/2023]
Abstract
Experimental evidence of vibrational resonance in a multistable vertical-cavity surface-emitting laser (VCSEL) is reported. The VCSEL is characterized by a coexistence of four polarization states and driven by low-frequency (LF) and high-frequency (HF) periodic signals. In these conditions a series of resonances on the low frequency depending on the HF amplitude is observed. The location of resonances in a parameter space (dc current, amplitude of HF signal) is experimentally studied. For a fixed value of the dc current an evolution of the resonance curves with an increase of the LF amplitude is experimentally investigated.
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Affiliation(s)
- V N Chizhevsky
- B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 220072 Minsk, Belarus
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