Multiple Vibrational Resonances Research Articles

Effects of electric field on vibrational resonance in Izhikevich neuronal systems

In this paper, based on the Izhikevich neuron model, the effects of electric field (EF) on vibrational resonance (VR) of single neuron and bidirectionally coupled neurons system are investigated. It is found that multiple vibrational resonances (MVR) can be observed in a single Izhikevich neuron model whether EF is considered or not. After the introduction of EF, the system exhibits worse MVR and local vibrational anti-resonance can be observed. In coupled neuronal system, the effect of bidirectional coupling causes MVR to disappear and the system only exhibits the phenomenon of VR. When EF is not considered, the vibrational anti-resonance is also observed. Interestingly, the introduction of EF weakens both VR and anti-resonance in the system. In addition, the effects of system parameters such as the EF strength controller and coupling strength on the Fourier coefficients are also investigated, and it is found that these parameters can also cause changes in the number of resonance peaks, resulting in vibrational bi-resonance and vibrational triple-resonance. The EF plays an important role in attenuating VR in neuronal systems. Therefore, this study can provide new insights for further control of abnormal electrical activities and information transmission in neurons.

Effects of electric field on multiple vibrational resonances in Hindmarsh-Rose neuronal systems

• The effect of electric field plays an important role in the electrical activities of neuronal systems. • Vibration resonance is widely used in weak signal detection and propagation. • The electric field weakens the multiple vibrational resonance of a single • Hindmarsh-Rose (HR) ne4uron, but enhances the multiple vibrational resonance of the coupled HR neuron system. • Multiple vibrational resonances implies the matching of multiple frequencies giving rise to an enhanced response. • Anti-resonance has certain practical significance in reducing some unexpected vibration in the field of aerospace engineering and machinery The effects of electric field on vibrational resonance in single Hindmarsh-Rose (HR) neuron and coupled HR neurons system are investigated by using Fourier coefficient, respectively. It is found that the multiple vibrational resonances (MVR) can be observed in a single HR neuron model no matter the electric field is considered or not, and the electric field weakens the MVR. When bidirectional coupling between two HR neurons is considered, the occurrence of MVR can also be detected, it is very interesting to observe that the electric field can enhance the MVR. The higher the frequency of the low-frequency signal is, the less the number of resonance peaks of the system response to the low-frequency signal will be. Moreover, the local anti-resonance is also observed when appropriate parameters are selected. The effects of coupling strength and other system parameters on Fourier coefficient are also illustrated here. The systems manifesting MVR have better capacity for detecting and propagating signals.

Occurrence of Vibrational resonance in an oscillator with an asymmetric Toda potential

Vibrational resonance (VR) is a phenomenon wherein the response of a nonlinear oscillator driven by biharmonic forces with two different frequencies, ω and Ω, such that Ω≫ω, is enhanced by optimizing the parameters of high-frequency driving force. In this paper, an counterintuitive scenario in which a biharmonically driven nonlinear oscillator does not vibrate under the well known VR conditions is reported. This behaviour was observed in a system with an integrable and asymmetric Toda potential driven by biharmonic forces in the usual VR configuration. It is shown that with constant dissipation and in the presence of biharmonic forces, VR does not take place, whereas with nonlinear displacement-dependent periodic dissipation multiple VR can be induced at certain values of high-frequency force parameters. Theoretical analysis are validated using numerical computation and Simulink implementation in MATLAB. Finally, the regime in parameter space of the dissipation for optimum occurrence of multiple VR in the Toda oscillator was estimated. This result would be relevant for experimental applications of dual-frequency driven laser models where the Toda potential is extensively employed.

Multiple vibrational resonance and antiresonance in a coupled anharmonic oscillator under monochromatic excitation

We examine the existence of multiple vibrational resonance (VR) and antiresonance in two coupled overdamped anharmonic oscillators where each one is individually driven by a monochromatic sinusoidal signal with widely separated frequencies ( $$\Omega \gg \omega $$ ). In contemporary VR, superposed periodic waves are adopted to infer resonance, but herein we employ non-superposed periodic waves to acquire the elevated response. We study two coupling schemes namely, unidirectional and bidirectional, to substantiate the occurrence of multiple VR and antiresonance. Such occurrences have been shown and the results were ascertained with supportive numerical and experimental outcomes. We also illustrate the effect of coupling strength on the observed phenomenon.

Enhanced multiple vibrational resonances by Na+ and K+ dynamics in a neuron model.

Some neuronal receptors perceive external input in the form of hybrid periodic signals. The signal detection may be based on the mechanism of vibrational resonance, in which a system's response to the low frequency signal can become optimal by an appropriate choice of the vibration amplitude of HFS. The vibrational resonance effect is investigated in a neuron model in which the intra- and extra-cellular potassium and sodium concentrations are allowed to evolve temporally, depending on ion currents, Na+-K+ pumps, glial buffering, and ion diffusion. Our results reveal that, compared to the vibrational resonances in the model with constant ion concentrations, the significantly enhanced vibrational multi-resonances can be observed for the single neuron system where the potassium and sodium ion concentrations vary temporally. Thus, in contradiction to a popular view that ion concentrations dynamics play little role in signal detection, we indicate that the neuron's response to an external subthreshold signal can be largely improved by sodium and potassium dynamics.

Delay-enhanced signal transmission in a coupled excitable system

In the present paper, the phenomenon of the low-frequency signal transmission in a delayed coupling excitable system is investigated. Based on the mechanism of vibrational resonance (VR), the signal transmission is enhanced significantly by adjusting the time-delay feedback. Via numerical simulation, it is found that the multiple VR is induced by modulating the delay time. As expected, the phenomenon that the resonances of the first neuron and the others are synchronous is learned under the condition that the coupling strength is strong enough. In addition, with the aid of vibration resonance, the coupling strength is also helpful to the signal transmission process. Finally, we also find that because of the cooperation between the time-delay feedback and the high-frequency signal, the weak low-frequency signal can be transmitted with a much higher efficiency than the corresponding in an ordinary system.

Phase‐shaping strategies for coherent anti‐Stokes Raman scattering

AbstractThe identification of large molecules in complex environments requires probing of multiple vibrational resonances rather than a single resonance. Phase‐shaping the excitation pulses allows the coherent mixing of several resonances so that the presence of molecules can be inferred directly from the integrated output pulse energy. This avoids the need for the collection of spectra or multiple measurements. This article describes a particular implementation for coherent anti‐Stokes Raman scattering microscopy that uses a broadband pump and probe field in combination with a narrowband Stokes field. We numerically study the possibilities of optimizing selectivity, specificity, and sensitivity by precalculating pulse shapes using an evolutionary algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

Coherent control of vibrational transitions: Discriminating molecules in mixtures

Identifying complex molecules often entails detection of multiple vibrational resonances, especially in the case of mixtures. Phase shaping of broadband pump and probe pulses allows for the coherent superposition of several resonances, such that specific molecules can be detected directly and with high selectivity. Our particular implementation of coherent anti-Stokes Raman scattering (CARS) spectroscopy and imaging employs broadband pump and probe fields in combination with a narrowband Stokes field. We describe our approach for combining spectral phase shaping and closed-loop optimization strategies to perform chemically-selective microscopy. To predict the optimal excitation profile we employ evolutionary algorithms that use the vibrational phase responses of five distinct molecules with overlapping resonances and investigate the effect of phase instability on the optimization. We have recently shown that modified polynomials and orthogonal rational functions can give rise to improved contours for CARS fitness landscapes. Now, by considering the landscapes associated with different basis sets, we introduce two figures of merit to quantitatively rank basis functions in terms of their "appropriateness" for modeling nonlinear phase-shaped processes.

Controlling vibrational resonance in a multistable system by time delay

The phenomenon of vibrational resonance in a delayed multistable system that is excited by biharmonic signals is investigated in the present paper. Different from the former theory, the appearance and the disappearance of the vibrational resonance are controlled by adjusting the time delay parameter instead of modulating the amplitude of the high-frequency signal. The motion of the orbit within or between the different potential wells can also be controlled. Furthermore, based on both the methods of numerical simulation and analytical analysis, the behavior of delay-induced multiple vibrational resonance and its mechanism are investigated and discussed. The multiple vibrational resonance, which is quantified by the response amplitude at the low-frequency, is found to be periodic in the delay parameter with two periods, i.e., the periods of the two driven signals. The method used in this paper gives a new way for controlling vibrational resonance in a multistable system.

Single and multiple vibrational resonance in a quintic oscillator with monostable potentials

We analyze the occurrence of vibrational resonance in a damped quintic oscillator with three cases of single well of the potential V(x)=1/2omega(0)(2)x(2)+1/4betax(4)+1/6gammax(6) driven by both low-frequency force f cos omegat and high-frequency force g cos Omegat with Omega >> omega. We restrict our analysis to the parametric choices (i) omega(0)(2), beta, gamma > 0 (single well), (ii) omega(0)(2), gamma > 0, beta < 0, beta(2) < 4omega(0)(2)gamma (single well), and (iii) omega(0)(2) > 0, beta arbitrary, gamma < 0 (double-hump single well). From the approximate theoretical expression of response amplitude Q at the low-frequency omega we determine the values of omega and g (denoted as omega(VR) and g(VR)) at which vibrational resonance occurs. We show that for fixed values of the parameters of the system when omega is varied either resonance does not occur or it occurs only once. When the amplitude g is varied for the case of the potential with the parametric choice (i) at most one resonance occur while for the other two choices (ii) and (iii) multiple resonance occur. Further, g(VR) is found to be independent of the damping strength d while omega(VR) depends on d. The theoretical predictions are found to be in good agreement with the numerical result. We illustrate that the vibrational resonance can be characterized in terms of width of the orbit also.

In-vivo multi-nonlinear optical imaging of a living cell using a supercontinuum light source generated from a photonic crystal fiber

A supercontinuum light source generated with a femtosecond Ti:Sapphire oscillator has been used to obtain both vibrational and two-photon excitation fluorescence (TPEF) images of a living cell simultaneously at different wavelengths. Owing to an ultrabroadband spectral profile of the supercontinuum, multiple vibrational resonances have been detected through coherent anti-Stokes Raman scattering (CARS) process. In addition to the multiplex CARS process, multiple electronic states can be excited due to the broadband electronic two-photon excitation using the supercontinuum, giving rise to a two-photon excitation fluorescence (TPEF) signal. Using a living yeast cell whose nucleus is labeled by green fluorescent protein (GFP), we have succeeded in visualizing organelles such as mitochondria, septum, and nucleus through the CARS and the TPEF processes. The supercontinuum enables us to perform unique multi-nonlinear optical imaging through two different nonlinear optical processes.

Multiple vibrational resonances in the Raman spectra of liquid ethanes

AbstractThe Raman spectra of liquid ethane, ethane‐d3 and ethane‐d6 were recorded and analysed. The CH3 and CD3 stretching regions were computer resolved using Cauchy‐Gaussian and Voigt functions to account for asymmetric band shapes. Multiple vibrational resonances were investigated using the wavenumbers and observed intensities in these regions. The developed basis functions show strong mixing of the levels in these regions. In general the resonances appear to be less strong in the liquid phase than reported in previous studies of the gaseous state. Some new assignments in the liquid‐state spectra of ethanes could be suggested.

Experimental determination of CH-stretching–bending–bending cubic force constants of ethane from Raman intensity analysis

The vibrational anharmonicity of ethane has been experimentally investigated by means of a joint analysis of the gas-phase mean polarizability Raman scattering cross sections and the wave numbers of the multiple vibrational resonances in the C–H or C–D stretching region of several isotopic derivatives. Thirty nine cubic force constants krst in the representation of normal coordinates were obtained in a first step. In a second step they were reduced to a smaller set of isotopically invariant cubic constants Fijk in the representation of curvilinear symmetry coordinates.