Analysis of Vibrational Resonance in a Biophysical System
Main Article Content
Abstract
Living systems are composed of molecules and atoms that can exhibit specific quantum effects, including coherent electric vibration, and vibrating systems that undergo resonance. Due to their resonance, biological materials can transfer energy when they vibrate at a specific frequency. In this paper, we establish the occurrence of vibrational resonance in a biophysical system modeling activated enzyme molecules in the brain waves. The VR was characterised using the response amplitude, Q which was numerically calculated using the Fourier coefficient of the output signal. The external high-frequency signal affected the enzyme-substrate reaction and amplified the combination process observed at resonance. Importantly, double resonances were induced by the strength of the decay rate. Resonance, induced by the strength of the decay rate and the external high-frequency signal would lead to significant brain wave activity related to inherent energy transfers from changes to the decay rate, and enzyme-substrate combination, and could be observed from the Electroencephalogram.
Downloads
Article Details
References
Calim, A., Palabas, T., and Uzuntarla, M. (2021). Stochastic and vibrational resonance in complex networks of neurons. Philosophical Transactions of the Royal Society A, 379(2198):20200236.
Chizhevsky, V. (2021). Amplification of optical signals in a bistable vertical-cavity surface-emitting laser by vibrational resonance. Philosophical Transactions of the Royal Society A, 379(2192):20200241.
Chizhevsky, V. N. (2014). Experimental evidence of vibrational resonance in a multistable system. Physical Review E, 89:062914.
Chizhevsky, V. N. and Giacomelli, G. (2006). Experimental and theoretical study of vibrational resonance in a bistable system with asymmetry. Physical Review E, 73(2):022103.
Fr o¨hlich, H. (1968). Long range coherence and energy storage in biological systems. International Journal of Quantum Chemistry, 2:641-649.
Fu, P., Wang, C.-J., Yang, K.-L., Li, X.-B., and Yu, B. (2022). Reentrance-like vibrational resonance in a fractional-order birhythmic biological system. Chaos, Solitons and Fractals, 155:111649.
Gitterman, M. (2001). Bistable oscillator driven by two periodic fields. Journal of Physics A: Mathematical and General, 34(24):L355.
Jeyakumari, S., Chinnathambi, V., Rajasekar, S., and Sanjua´n, M. A. (2011). Vibrational resonance in an asymmetric duffing oscillator. International Journal of Bifurcation and Chaos, 21(01):275–286.
Jeyakumari, S., Chinnathambi, V., Rajasekar, S., and Sanjuan, M. A. F. (2009a). Analysis of vibrational resonance in a quintic oscillator. Chaos: An Interdisciplinary Journal of Nonlinear Science, 19(4):043128.
Jeyakumari, S., Chinnathambi, V., Rajasekar, S., and Sanjuan, M. A. F. (2009b). Single and multiple vibrational resonance in a quintic oscillator with monostable potentials. Physical Review E, 80(4):046608.
Kadji, H. E., Orou, J. C., Yamapi, R., and Woafo, P. (2007). Nonlinear dynamics and strange attractors in the biological system. Chaos, Solitons and Fractals, 32(2):862–882.
Kaiser, F. (1981a). Coherent excitations in biological systems: specific effects in externally driven self-sustained oscillating biophysical systems. Springer-Verlag, Berlin, Heidelberg.
Kaiser, F. (1981b). Coherent modes in biological systems. Biological effects of nonionizing radiation, 157:219.
Kaiser, F. and Eichwald, C. (1991). Bifurcation structure of a driven, multi-limit-cycle van der pol oscillator (i): The superharmonic resonance structure. International Journal of Bifurcation and Chaos, 1(02):485–491.
Morfu, S., Usama, B., and Marquie´, P. (2021). On some applications of vibrational resonance on noisy image perception: the role of the perturbation parameters. Philosophical Transactions of the Royal Society A, 379(2198):20200240.
Olusola, O., Shomotun, O., Vincent, U., and McClintock, P. (2020). Quantum vibrational resonance in a dual-frequency-driven Tietz-Hua quantum well. Physical Review E, 101(5):052216.
Omoteso, K. A., Roy-Layinde, T. O., Laoye, J. A., Vincent, U. E., and McClintock, P. V. E. (2021). Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator. Ultrasonics Sonochemistry, 70:105346.
Oyeleke K., Olusola, O., Vincent, U. E., Ghosh, D., and McClintock, P. V. (2021). Parametric vibrational resonance in a gyroscope driven by dual-frequency forces. Physics Letters A, 387:127040.
Pan, Y., Duan, F., Chapeau-Blondeau, F., Xu, L., and Abbott, D. (2021). Study of vibrational resonance in nonlinear signal processing. Philosophical Transactions of the Royal Society A, 379(2192):20200235.
Paul, S. and Shankar Ray, D. (2021). Vibrational resonance in a driven two-level quantum system, linear and nonlinear response. Philosophical Transactions of the Royal Society A, 379(2192):20200231.
Pereira, C. (2015). Biophysical understanding of resonance at a cellular level. Journal of
Metaphysics and Connected Consciousness Vol, 1:1–3.
Qiao, Z., Liu, J., Ma, X., and Liu, J. (2021). Double stochastic resonance induced by varying potential-well depth and width. Journal of the Franklin Institute, 358(3):2194–2211.
Qin, T., Xie, T., Luo, M., and Deng, K. (2017). Vibrational resonance in fractional-order overdamped multistable systems. Chinese Journal of Physics, 55(2):546–555.
Rajaseker, S., Abirami, K., and Sanjua´n, M. A. F. (2011). Novel vibrational resonance in multistable systems. Chaos, 21(3):033106.
Rajasekar, S. and Sanjuan, M. A. (2016). Nonlinear resonances. Springer.
Roy-Layinde, T. O., Laoye, J. A., Popoola, O. O., and Vincent, U. E. (2016). Analysis of vibrational resonance in bi-harmonically driven plasma. Chaos, 26(9):093117.
Roy-Layinde, T. O., Laoye, J. A., Popoola, O. O., Vincent, U. E., and McClintock, P. V. E. (2017). Vibrational resonance in an inhomogeneous medium with periodic dissipation. Physical Review E, 96:032209.
Roy-Layinde, T. O., Omoteso, K. A., Ogooluwa, D. O., Oladunjoye, H. T., and Laoye, J. A. (2020). Chaotic and periodic behavior in a fractional-order biological system. Acta Physica Polonica B, 51(9):1885-1904.
Roy-Layinde, T. O., Omoteso, K. A., Oyero, B. A., Laoye, J. A., and Vincent, U. E. (2022). Vibrational resonance of ammonia molecule with doubly singular position-dependent mass. The European Physical Journal B, 95(5):1–11.
Roy-Layinde, T. O., Omoteso, K. A., Diala, U. H., Runsewe, J. A., and Laoye, J. A. (2024). Analysis of vibrational resonance in an oscillator with exponential mass variation. Chaos, Solitons and Fractals, 178, 114310.
Sahoo, P. K. and Chatterjee, S. (2021). High-frequency vibrational control of principal parametric resonance of a nonlinear cantilever beam: Theory and experiment. Journal of Sound and Vibration, 505:116138.
Usama, B. I., Morfu, S., and Marquie´, P. (2019). Numerical analyses of the vibrational resonance occurrence in a nonlinear dissipative system. Chaos, Solitons and Fractals, 127:31–37.
Vincent, U. E., Roy-Layinde, T. O., Adesina, P. O., Popoola, O. O., and McClintock, P. V. E. (2018). Vibrational resonance in an oscillator with an asymmetrical deformable potential. Physical Review E, 98:062203.
Vincent, U. E., McClintock, P. V., Khovanov, I., and Rajasekar, S. (2021). Vibrational and stochastic resonances in driven nonlinear systems.
Yan, Z., Wang, W., and Liu, X. (2018). Analysis of a quintic system with fractional damping in the presence of vibrational resonance. Applied Mathematics and Computation, 321:780–793.
Yang J. H. and Liu, X. B. (2010). Controlling vibrational resonance in a multistable system by time delay. Chaos, 20(3):033124.
Yang, W. (2012). Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions. Computational and Applied Mathematics, 63:288–297.
Yang, J., Rajasekar, S., and Sanjuán, M. A. (2024). Vibrational resonance: A review. Physics Reports, 1067, 1-62.
Yao, C. and Zhan, M. (2010). Signal transmission by vibrational resonance in one-way coupled bistable systems. Physical Review E, 81(6):061129.
Yu, H., Wang, J., Liu, C., Deng, B., and Wei, X. (2011). Vibrational resonance in excitable neuronal systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21(4):043101.