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Ashokkumar P, Kabilan R, Sathish Aravindh M, Venkatesan A, Lakshmanan M. Harnessing vibrational resonance to identify and enhance input signals. CHAOS (WOODBURY, N.Y.) 2024; 34:013129. [PMID: 38252785 DOI: 10.1063/5.0169195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 12/21/2023] [Indexed: 01/24/2024]
Abstract
We report the occurrence of vibrational resonance and the underlying mechanism in a simple piecewise linear electronic circuit, namely, the Murali-Lakshmanan-Chua circuit, driven by an additional biharmonic signal with widely different frequencies. When the amplitude of the high-frequency force is tuned, the resultant vibrational resonance is used to detect the low-frequency signal and also to enhance it into a high-frequency signal. Further, we also show that even when the low-frequency signal is changed from sine wave to square and sawtooth waves, vibrational resonance can be used to detect and enhance them into high-frequency signals. These behaviors, confirmed by experimental results, are illustrated with appropriate analytical and numerical solutions of the corresponding circuit equations describing the system. Finally, we also verify the signal detection in the above circuit even with the addition of noise.
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Affiliation(s)
- P Ashokkumar
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
| | - R Kabilan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Sathish Aravindh
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
| | - A Venkatesan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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Calim A, Longtin A, Uzuntarla M. Vibrational resonance in a neuron-astrocyte coupled model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200267. [PMID: 33840211 DOI: 10.1098/rsta.2020.0267] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/28/2020] [Indexed: 05/22/2023]
Abstract
Recent findings have revealed that not only neurons but also astrocytes, a special type of glial cells, are major players of neuronal information processing. It is now widely accepted that they contribute to the regulation of their microenvironment by cross-talking with neurons via gliotransmitters. In this context, we here study the phenomenon of vibrational resonance in neurons by considering their interaction with astrocytes. Our analysis of a neuron-astrocyte pair reveals that intracellular dynamics of astrocytes can induce a double vibrational resonance effect in the weak signal detection performance of a neuron, exhibiting two distinct wells centred at different high-frequency driving amplitudes. We also identify the underlying mechanism of this behaviour, showing that the interaction of widely separated time scales of neurons, astrocytes and driving signals is the key factor for the emergence and control of double vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.
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Affiliation(s)
- Ali Calim
- Department of Biomedical Engineering, Zonguldak Bulent Ecevit University, Zonguldak, Turkey
| | - Andre Longtin
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada
| | - Muhammet Uzuntarla
- Department of Biomedical Engineering, Zonguldak Bulent Ecevit University, Zonguldak, Turkey
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Sorokin V, Demidov I. On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200229. [PMID: 33455556 DOI: 10.1098/rsta.2020.0229] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/26/2020] [Indexed: 05/22/2023]
Abstract
Adding noise to a system can 'improve' its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this 'deterministic' approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
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Affiliation(s)
- V Sorokin
- Department of Mechanical Engineering, University of Auckland, Bldg 405 Level 8, Room 851, Auckland 1010, New Zealand
| | - I Demidov
- Mehanobr-Tekhnika Research and Engineering Corp. 3, 22 Liniya, V.O., St. Petersburg, Russia 199106
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Kremer E. The effect of high-frequency stochastic actions on the low-frequency behaviour of dynamic systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200242. [PMID: 33455550 DOI: 10.1098/rsta.2020.0242] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/22/2020] [Indexed: 05/22/2023]
Abstract
The dynamic system described by a finite number of first-order differential equations is considered. The right side of each equation is a sum of a slow, deterministic and, in the general case, nonlinear function of dynamic variables and a stochastic excitation. The stochastic action is a superposition of a finite number of independent random processes with coefficients depending on dynamic variables and slow time. The problem statement is oriented to applications in the field of driven systems. The analysis is based on the concept of vibration mechanics proposed by I. I. Blekhman. The modified method of direct separation of slow and fast motions uses the explicit introduction of a small parameter and some ideas of the two-scale technique. The general formulas for vibrational forces (or fluxes) are obtained. These additional terms appear in the resulting system for averaged motion instead of the stochastic terms to make the averaged system equivalent to the initial stochastic system with respect to slow motions and, in particular, to low-frequency resonances. As an example, the model of a vibration machine for bulk material processing is considered. The stochastic effect is caused by random oscillations of the bulk material mass. It is transformed into a modification of the machine's frequency characteristics leading to a specific stochastic resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
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Affiliation(s)
- Eugen Kremer
- REC Mekhanobr-tekhnika, V.O., 22 Linija, 3, St Petersburg 199106, Russia
- Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, V.O. Bolshoj pr. 61, St Petersburg 199178, Russia
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Roy-Layinde TO, Vincent UE, Abolade SA, Popoola OO, Laoye JA, McClintock PVE. Vibrational resonances in driven oscillators with position-dependent mass. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200227. [PMID: 33455553 DOI: 10.1098/rsta.2020.0227] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/25/2020] [Indexed: 05/22/2023]
Abstract
The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM). We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework for determining the response amplitude of PDM systems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
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Affiliation(s)
- T O Roy-Layinde
- 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, UK
| | - S A Abolade
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - O O Popoola
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
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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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Olusola OI, Shomotun OP, Vincent UE, McClintock PVE. Quantum vibrational resonance in a dual-frequency-driven Tietz-Hua quantum well. Phys Rev E 2020; 101:052216. [PMID: 32575245 DOI: 10.1103/physreve.101.052216] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 05/12/2020] [Indexed: 06/11/2023]
Abstract
We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude |s|^{2} under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, |s|^{2} shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in |s|^{2}. However, the |s|^{2} maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.
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Affiliation(s)
- O I Olusola
- Department of Physics, University of Lagos, Lagos, Nigeria
| | - O P Shomotun
- Department of Physics, University of Lagos, Lagos, 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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