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Effects of high–low-frequency electromagnetic radiation on vibrational resonance in FitzHugh–Nagumo neuronal systems

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

In this paper, based on the modified FitzHugh–Nagumo (FHN) neuron model, the effects of high–low-frequency (HLF) electromagnetic radiation on vibrational resonance (VR) in single neuron and two coupled neurons system are investigated, respectively. It is found that the VR can be observed in a single modified FHN neuron model with or without considering the HLF electromagnetic radiation, and the HLF electromagnetic radiation weakens the VR. When coupling between two modified FHN neurons is considered, the multiple vibrational resonances (MVR) can be detected. However, the input of HLF electromagnetic radiation makes the maximum area and intensity of the system response amplitude smaller, ultimately weakening the MVR. Further analysis shows that the HLF electromagnetic radiation caused a decrease in the number and amplitude of neuronal discharges, making the system less sensitive to the low-frequency signal, thus weakening the VR. In addition, the effects of system parameters such as the amplitude and frequency of HLF electromagnetic radiation and the strength of coupling between two neurons on the Fourier coefficients are investigated, and it is found that these parameters can also induce changes in the number of resonance peaks, resulting in VR and MVR. Systems that exhibit MVR have better ability to detect and propagate signals under HLF electromagnetic radiation. And the HLF electromagnetic radiation plays an important role in weakening the VR in neuronal systems.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. S. Fauve, F. Heslot, Stochastic resonance in a bistable system. Phys. Lett. A 97(1–2), 5–7 (1983). https://doi.org/10.1016/0375-9601(83)90086-5

    Article  ADS  Google Scholar 

  2. N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, G. Matsumoto, Global bifurcation structure in periodically stimulated giant axons of squid. Phys. D 43(2–3), 318–334 (1990). https://doi.org/10.1016/0167-2789(90)90140-K

    Article  MATH  Google Scholar 

  3. P. Hänggi, Stochastic resonance in biology how noise can enhance detection of weak signals and help improve biological information processing. ChemPhysChem 3(3), 285–290 (2002). https://doi.org/10.1002/1439-7641(20020315)3:3<285::AID-CPHC285>3.0.CO;2-A

    Article  Google Scholar 

  4. R. Benzi, A. Sutera, A. Vulpiani, The mechanism of stochastic resonance. J. Phys. A: Math. Gen. 14(11), 453 (1981). https://doi.org/10.1088/0305-4470/14/11/006

    Article  ADS  MathSciNet  Google Scholar 

  5. R. Benzi, Stochastic resonance: from climate to biology. Nonlinear Process. Geophys. 17(5), 431–441 (2010). https://doi.org/10.5194/npg-17-431-2010

    Article  ADS  Google Scholar 

  6. J. Gao, J. Yang, D. Huang, H. Liu, S. Liu, Experimental application of vibrational resonance on bearing fault diagnosis. J. Braz. Soc. Mech. Sci. Eng. 41, 1–13 (2019). https://doi.org/10.1007/s40430-018-1502-0

    Article  Google Scholar 

  7. V.N. Chizhevsky, G. Giacomelli, Experimental and theoretical study of vibrational resonance in a bistable system with asymmetry. Phys. Rev. E 73(2), 022103 (2006). https://doi.org/10.1103/PhysRevE.73.022103

    Article  ADS  Google Scholar 

  8. M.D. McDonnell, D. Abbott, What is stochastic resonance? definitions, misconceptions, debates, and its relevance to biology. PLoS Comput. Biol. 5(5), 1000348 (2009). https://doi.org/10.1371/journal.pcbi.1000348

    Article  ADS  MathSciNet  Google Scholar 

  9. B. Hutcheon, Y. Yarom, Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci. 23(5), 216–222 (2000). https://doi.org/10.1016/S0166-2236(00)01547-2

    Article  Google Scholar 

  10. B.J. Gluckman, T.I. Netoff, E.J. Neel, W.L. Ditto, M.L. Spano, S.J. Schiff, Stochastic resonance in a neuronal network from mammalian brain. Phys. Rev. Lett. 77(19), 4098 (1996). https://doi.org/10.1103/PhysRevLett.77.4098

    Article  ADS  Google Scholar 

  11. D. Guo, C. Li, Stochastic resonance in hodgkin-huxley neuron induced by unreliable synaptic transmission. J. Theor. Biol. 308, 105–114 (2012). https://doi.org/10.1016/j.jtbi.2012.05.034

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. A. Bulsara, E.W. Jacobs, T. Zhou, F. Moss, L. Kiss, Stochastic resonance in a single neuron model: Theory and analog simulation. J. Theor. Biol. 152(4), 531–555 (1991). https://doi.org/10.1016/S0022-5193(05)80396-0

    Article  ADS  Google Scholar 

  13. A. Longtin, Stochastic resonance in neuron models. J. Stat. Phys. 70, 309–327 (1993). https://doi.org/10.1007/BF01053970

    Article  ADS  MATH  Google Scholar 

  14. D. Nozaki, D.J. Mar, P. Grigg, J.J. Collins, Effects of colored noise on stochastic resonance in sensory neurons. Phys. Rev. Lett. 82(11), 2402 (1999). https://doi.org/10.1103/PhysRevLett.82.2402

    Article  ADS  Google Scholar 

  15. J.J. Collins, C.C. Chow, T.T. Imhoff, Stochastic resonance without tuning. Nature 376, 236–238 (1995)

    Article  ADS  Google Scholar 

  16. M., P, Stochastic resonance on excitable small-world networks via a pacemaker. Phys 76(6), 066203 (2007) https://doi.org/10.1103/PhysRevE.76.066203

  17. S.M. Bezrukov, I. Vodyanoy, Noise-induced enhancement of signal transduction across voltage-dependent ion channels. Nature 378(6555), 362–364 (1995). https://doi.org/10.1038/378362a0

    Article  ADS  Google Scholar 

  18. Y. Xu, Y. Guo, G. Ren, J. Ma, Dynamics and stochastic resonance in a thermosensitive neuron. Appl. Math. Comput. 385, 125427 (2020). https://doi.org/10.1016/j.amc.2020.125427

    Article  MathSciNet  MATH  Google Scholar 

  19. A.R. Bulsara, A.J. Maren, G. Schmera, Single effective neuron: Dendritic coupling effects and stochastic resonance. Biol. Cybern. 70(2), 145–156 (1993). https://doi.org/10.1007/BF00200828

    Article  MATH  Google Scholar 

  20. T. Palabas, J.J. Torres, M. Perc, M. Uzuntarla, Double stochastic resonance in neuronal dynamics due to astrocytes. Chaos, Solitons Fractals 168, 113140 (2023). https://doi.org/10.1016/j.chaos.2023.113140

    Article  Google Scholar 

  21. G. Wang, Y. Wu, F. Xiao, Z. Ye, Y. Jia, Non-gaussian noise and autapse-induced inverse stochastic resonance in bistable izhikevich neural system under electromagnetic induction. Phys. A 598, 127274 (2022). https://doi.org/10.1016/j.physa.2022.127274

    Article  MathSciNet  MATH  Google Scholar 

  22. N. Salansky, A. Fedotchev, A. Bondar, Responses of the nervous system to low frequency stimulation and eeg rhythms: clinical implications. Neurosci. Biobehav. Rev. 22(3), 395–409 (1998). https://doi.org/10.1016/S0149-7634(97)00029-8

    Article  Google Scholar 

  23. Q. Lu, H. Gu, Z. Yang, X. Shi, L. Duan, Y. Zheng, Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis. Acta. Mech. Sin. 24(6), 593–628 (2008). https://doi.org/10.1007/s10409-008-0204-8

    Article  ADS  MATH  Google Scholar 

  24. Y. Eroglu, M. Yildirim, A. Cinar, mrmr-based hybrid convolutional neural network model for classification of alzheimer’s disease on brain magnetic resonance images. Int. J. Imaging Syst. Technol. 32(2), 517–527 (2022). https://doi.org/10.1002/ima.22632

    Article  Google Scholar 

  25. J. Zhu, C. Kong, L. X., Subthreshold and suprathreshold vibrational resonance in the fitzhugh-nagumo neuron model. Phys. Rev. E 94(3), 032208 (2016) https://doi.org/10.1103/PhysRevE.94.032208

  26. E. Ullner, A. Zaikin, J. García-Ojalvo, R. Báscones, J. Kurths, Vibrational resonance and vibrational propagation in excitable systems. Phys. Lett. A 312(5–6), 348–354 (2003). https://doi.org/10.1016/S0375-9601(03)00681-9

    Article  ADS  MathSciNet  Google Scholar 

  27. J.P. Baltanás, L. López, I.I. Blechman, P.S. Landa, A. Zaikin, J. Kurths, M.A.F. Sanjuán, Experimental evidence, numerics, and theory of vibrational resonance in bistable systems. Phys. Rev. E 67(6), 066119 (2003). https://doi.org/10.1103/PhysRevE.67.066119

    Article  ADS  Google Scholar 

  28. P.S. Landa, Vibrational resonance. J. Phys. A: Math. Gen. 33(45), 433 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  29. S. Jeyakumari, V. Chinnathambi, S. Rajasekar, M.A.F. Sanjuan, Single and multiple vibrational resonance in a quintic oscillator with monostable potentials. Phys. Rev. E 80(4), 046608 (2009). https://doi.org/10.1103/PhysRevE.80.046608

    Article  ADS  Google Scholar 

  30. A. Calim, A. Longtin, M. Uzuntarla, Vibrational resonance in a neuron-astrocyte coupled model. Philos. Trans. R. Soc. A 379(2198), 20200267 (2021). https://doi.org/10.1098/rsta.2020.0267

    Article  ADS  Google Scholar 

  31. B. Deng, J. Wang, X. Wei, Effect of chemical synapse on vibrational resonance in coupled neurons. Chaos 19(1), 013117 (2009). https://doi.org/10.1063/1.3076396

    Article  ADS  Google Scholar 

  32. B. Deng, J. Wang, X. Wei, K.M. Tsang, W.L. Chan, Vibrational resonance in neuron populations. Chaos 20(1), 013113 (2010). https://doi.org/10.1063/1.3324700

    Article  ADS  Google Scholar 

  33. A. Calim, T. Palabas, M. Uzuntarla, Stochastic and vibrational resonance in complex networks of neurons. Philos. Trans. R. Soc. A 379(2198), 20200236 (2021). https://doi.org/10.1098/rsta.2020.0236

    Article  ADS  Google Scholar 

  34. S.N. Agaoglu, A. Calim, P. Hövel, M. Ozer, M. Uzuntarla, Vibrational resonance in a scale-free network with different coupling schemes. Neurocomputing 325, 59–66 (2019). https://doi.org/10.1016/j.neucom.2018.09.070

    Article  Google Scholar 

  35. A.A. Zaikin, L. López, J.P. Baltanás, J. Kurths, M.A.F. Sanjuán, Vibrational resonance in a noise-induced structure. Phys. Rev. E 66(1), 011106 (2002). https://doi.org/10.1103/PhysRevE.66.011106

    Article  ADS  Google Scholar 

  36. C. Wang, K. Yang, S. Qu, Vibrational resonance in a discrete neuronal model with time delay. Int. J. Mod. Phys. B 28(16), 1450103 (2014). https://doi.org/10.1142/S0217979214501033

    Article  ADS  MathSciNet  Google Scholar 

  37. D. Hu, J. Yang, X. Liu, Delay-induced vibrational multiresonance in fitzhugh-nagumo system. Commun. Nonlinear Sci. Numer. Simul. 17(2), 1031–1035 (2012). https://doi.org/10.1016/j.cnsns.2011.05.041

    Article  ADS  MathSciNet  Google Scholar 

  38. L. Yang, W. Liu, M. Yi, C. Wang, Q. Zhu, X. Zhan, Y. Jia, Vibrational resonance induced by transition of phase-locking modes in excitable systems. Phys. Rev. E 86(1), 016209 (2012). https://doi.org/10.1103/PhysRevE.86.016209

    Article  ADS  Google Scholar 

  39. L. Chua, Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971). https://doi.org/10.1109/TCT.1971.1083337

    Article  Google Scholar 

  40. D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature 453(7191), 80–83 (2008). https://doi.org/10.1038/nature06932

    Article  ADS  Google Scholar 

  41. C. Wang, M. Lv, A. Alsaedi, J. Ma, Synchronization stability and pattern selection in a memristive neuronal network. Chaos 27(11), 113108 (2017). https://doi.org/10.1063/1.5004234

    Article  ADS  MathSciNet  Google Scholar 

  42. K. Rajagopal, F. Parastesh, H. Azarnoush, B. Hatef, S. Jafari, V. Berec, Spiral waves in externally excited neuronal network: Solvable model with a monotonically differentiable magnetic flux. Chaos 29(4), 043109 (2019). https://doi.org/10.1063/1.5088654

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. W. Yao, C. Wang, J. Cao, Y. Sun, C. Zhou, Hybrid multisynchronization of coupled multistable memristive neural networks with time delays. Neurocomputing 363, 281–294 (2019). https://doi.org/10.1016/j.neucom.2019.07.014

    Article  Google Scholar 

  44. C. Wang, L. Xiong, J. Sun, W. Yao, Memristor-based neural networks with weight simultaneous perturbation training. Nonlinear Dyn. 95(4), 2893–2906 (2019). https://doi.org/10.1007/s11071-018-4730-z

    Article  Google Scholar 

  45. D.B. SStrukov, Endurance-write-speed tradeoffs in nonvolatile memories. Appl. Phys. A 122, 1–4 (2016). https://doi.org/10.1007/s00339-016-9841-0

    Article  Google Scholar 

  46. S. Kvatinsky, M. Ramadan, E.G. Friedman, A. Kolodny, Vteam: A general model for voltage-controlled memristors. IEEE Trans. Circuits Syst. II Express Briefs 62(8), 786–790 (2015). https://doi.org/10.1109/TCSII.2015.2433536

    Article  Google Scholar 

  47. J. Ruan, K. Sun, J. Mou, S. He, L. Zhang, Fractional-order simplest memristor-based chaotic circuit with new derivative. Eur. Phys. J. Plus 133, 1–12 (2018). https://doi.org/10.1140/epjp/i2018-11828-0

    Article  Google Scholar 

  48. L. Zhou, C. Wang, L. Zhou, A novel no-equilibrium hyperchaotic multi-wing system via introducing memristor. Int. J. Circuit Theory Appl. 46(1), 84–98 (2018). https://doi.org/10.1002/cta.2339

    Article  Google Scholar 

  49. C. Wang, X. Liu, H. Xia, Multi-piecewise quadratic nonlinearity memristor and its 2 n-scroll and 2 n+ 1-scroll chaotic attractors system. Chaos 27(3), 033114 (2017). https://doi.org/10.1063/1.4979039

    Article  ADS  MATH  Google Scholar 

  50. F. Yu, Z. Zhang, L. Liu, H. Shen, Y. Huang, C. Shi, S. Cai, Y. Song, S. Du, Q. Xu, Secure communication scheme based on a new 5d multistable four-wing memristive hyperchaotic system with disturbance inputs. Complexity 2020, 1–16 (2020). https://doi.org/10.1155/2020/5859273

    Article  ADS  MATH  Google Scholar 

  51. X. Xie, S. Wen, Z. Zeng, T. Huang, Memristor-based circuit implementation of pulse-coupled neural network with dynamical threshold generators. Neurocomputing 284, 10–16 (2018). https://doi.org/10.1016/j.neucom.2018.01.024

    Article  Google Scholar 

  52. S. Wen, X. Xie, Z. Yan, T. Huang, Z. Zeng, General memristor with applications in multilayer neural networks. Neural Netw. 103, 142–149 (2018). https://doi.org/10.1016/j.neunet.2018.03.015

    Article  Google Scholar 

  53. D. Soudry, D. Di Castro, A. Gal, A. Kolodny, S. Kvatinsky, Memristor-based multilayer neural networks with online gradient descent training. IEEE Trans Neural Netw Learn Syst 26(10), 2408–2421 (2015). https://doi.org/10.1109/TNNLS.2014.2383395

    Article  MathSciNet  Google Scholar 

  54. Y.V. Pershin, M. Di Ventra, Experimental demonstration of associative memory with memristive neural networks. Neural Netw. 23(7), 881–886 (2010). https://doi.org/10.1016/j.neunet.2010.05.001

    Article  Google Scholar 

  55. G. Ren, Y. Xu, C. Wang, Synchronization behavior of coupled neuron circuits composed of memristors. Nonlinear Dyn. 88, 893–901 (2017). https://doi.org/10.1007/s11071-016-3283-2

    Article  Google Scholar 

  56. A. Thomas, Memristor-based neural networks. J. Phys. D Appl. Phys. 46(9), 093001 (2013). https://doi.org/10.1088/0022-3727/46/9/093001

    Article  ADS  Google Scholar 

  57. J. Ma, F. Wu, C. Wang, Synchronization behaviors of coupled neurons under electromagnetic radiation. Int. J. Mod. Phys. B 31(2), 1650251 (2017). https://doi.org/10.1142/S0217979216502519

    Article  ADS  MathSciNet  Google Scholar 

  58. Y. Xu, H. Ying, Y. Jia, J. Ma, T. Hayat, Autaptic regulation of electrical activities in neuron under electromagnetic induction. Sci. Rep. 7(1), 1–12 (2017). https://doi.org/10.1038/srep43452

    Article  Google Scholar 

  59. Y. Xu, Y. Jia, H. Wang, Y. Liu, P. Wang, Y. Zhao, Spiking activities in chain neural network driven by channel noise with field coupling. Nonlinear Dyn. 95, 3237–3247 (2019). https://doi.org/10.1007/s11071-018-04752-2

    Article  MATH  Google Scholar 

  60. Y. Xu, J. Ma, X. Zhan, L. Yang, Y. Jia, Temperature effect on memristive ion channels. Cogn. Neurodyn. 13, 601–611 (2019). https://doi.org/10.1007/s11571-019-09547-8

    Article  Google Scholar 

  61. M. Lv, C. Wang, G. Ren, J. Ma, X. Song, Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016). https://doi.org/10.1007/s11071-016-2773-6

    Article  Google Scholar 

  62. C.N. Takembo, A. Mvogo, H.P. Ekobena Fouda, T.C. Kofané, Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network. Nonlinear Dyn. 95, 1067–1078 (2019). https://doi.org/10.1007/s11071-018-4616-0

    Article  MATH  Google Scholar 

  63. C.N. Takembo, A. Mvogo, H.P. Ekobena Fouda, T.C. Kofané, Wave pattern stability of neurons coupled by memristive electromagnetic induction. Nonlinear Dyn. 96, 1083–1093 (2019). https://doi.org/10.1007/s11071-019-04841-w

    Article  Google Scholar 

  64. J. Ma, Y. Wang, C. Wang, Y. Xu, G. Ren, Mode selection in electrical activities of myocardial cell exposed to electromagnetic radiation. Chaos, Solitons Fractals 99, 219–225 (2017). https://doi.org/10.1016/j.chaos.2017.04.016

    Article  ADS  Google Scholar 

  65. Y. Xu, Y. Jia, J. Ma, A. Alsaedi, B. Ahmad, Synchronization between neurons coupled by memristor. Chaos, Solitons Fractals 104, 435–442 (2017). https://doi.org/10.1016/j.chaos.2017.09.002

    Article  ADS  Google Scholar 

  66. M. Ge, L. Lu, Y. Xu, R. Mamatimin, Q. Pei, Y. Jia, Vibrational mono-/bi-resonance and wave propagation in fitzhugh-nagumo neural systems under electromagnetic induction. Chaos, Solitons Fractals 133, 109645 (2020). https://doi.org/10.1016/j.chaos.2020.109645

    Article  MathSciNet  MATH  Google Scholar 

  67. F. Wu, C. Wang, W. Jin, J. Ma, Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Phys. A 469, 81–88 (2017). https://doi.org/10.1016/j.physa.2016.11.056

    Article  MathSciNet  MATH  Google Scholar 

  68. F. Li, C. Yao, The infinite-scroll attractor and energy transition in chaotic circuit. Nonlinear Dyn. 84, 2305–2315 (2016). https://doi.org/10.1007/s11071-016-2646-z

    Article  MathSciNet  Google Scholar 

  69. L. Lu, Y. Jia, M. Ge, Y. Xu, A. Li, Inverse stochastic resonance in hodgkin-huxley neural system driven by gaussian and non-gaussian colored noises. Nonlinear Dyn. 100, 877–889 (2020). https://doi.org/10.1007/s11071-020-05492-y

    Article  Google Scholar 

  70. C.N. Takembo, A. Mvogo, H.P. Ekobena Fouda, T.C. Kofané, Modulated wave formation in myocardial cells under electromagnetic radiation. Int. J. Mod. Phys. B 32(14), 1850165 (2018). https://doi.org/10.1142/S0217979218501655

    Article  ADS  MathSciNet  Google Scholar 

  71. B. Pol, Lxxxviii. on “relaxation-oscillations. Lond. Edinb. Dublin philos. mag. j. sci. 2(11), 978–992 (1926) https://doi.org/10.1080/14786442608564127

  72. R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane. Biophys. J . 1(6), 445–466 (1961). https://doi.org/10.1016/S0006-3495(61)86902-6

    Article  Google Scholar 

  73. J. Nagumo, S. Arimoto, S. Yoshizawa, An active pulse transmission line simulating nerve axon. Proc. IRE 50(10), 2061–2070 (1962). https://doi.org/10.1109/JRPROC.1962.288235

    Article  Google Scholar 

  74. H. Yu, J. Wang, B. Deng, X. Wei, Y. Che, Y.K. Wong, W.L. Chan, K.M. Tsang, Adaptive backstepping sliding mode control for chaos synchronization of two coupled neurons in the external electrical stimulation. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1344–1354 (2012). https://doi.org/10.1016/j.cnsns.2011.07.009

    Article  ADS  MathSciNet  MATH  Google Scholar 

  75. S. Baigent, Cells coupled by voltage-dependent gap junctions: the asymptotic dynamical limit. Biosystems 68(2–3), 213–222 (2003). https://doi.org/10.1016/S0303-2647(02)00097-7

    Article  Google Scholar 

  76. S. Zhou, W. Lin, Eliminating synchronization of coupled neurons adaptively by using feedback coupling with heterogeneous delays. Chaos 31(2), 023114 (2021). https://doi.org/10.1063/5.0035327

    Article  ADS  MathSciNet  MATH  Google Scholar 

  77. M. Ge, Y. Jia, L. Lu, Y. Xu, H. Wang, Y. Zhao, Propagation characteristics of weak signal in feedforward izhikevich neural networks. Nonlinear Dyn. 99, 2355–2367 (2020). https://doi.org/10.1007/s11071-019-05392-w

    Article  Google Scholar 

  78. G. Wang, D. Yu, Q. Ding, T. Li, Y. Jia, Effects of electric field on multiple vibrational resonances in hindmarsh-rose neuronal systems. Chaos, Solitons Fractals 150, 111210 (2021). https://doi.org/10.1016/j.chaos.2021.111210

    Article  MathSciNet  MATH  Google Scholar 

  79. V. Baysal, E. Yilmaz, Effects of electromagnetic induction on vibrational resonance in single neurons and neuronal networks. Phys. A 537, 122733 (2020). https://doi.org/10.1016/j.physa.2019.122733

    Article  MathSciNet  MATH  Google Scholar 

  80. T.O. Roy-Layinde, K.A. Omoteso, B.A. Oyero, J.A. Laoye, U.E. Vincent, Vibrational resonance of ammonia molecule with doubly singular position-dependent mass. Eur. Phys. J. B 95(5), 80 (2022). https://doi.org/10.1140/epjb/s10051-022-00342-9

  81. C. Dong, Y. Lan, Organization of spatially periodic solutions of the steady kuramoto-sivashinsky equation. Commun. Nonlinear Sci. Numer. Simul. 19(6), 2140–2153 (2014). https://doi.org/10.1016/j.cnsns.2013.09.040

    Article  ADS  MathSciNet  MATH  Google Scholar 

  82. M. Wechselberger, Canards. Scholarpedia 2(4), 1356 (2007). https://doi.org/10.4249/scholarpedia.1356

    Article  ADS  Google Scholar 

  83. X.X. Wu, C. Yao, J. Shuai, Enhanced multiple vibrational resonances by na+ and k+ dynamics in a neuron model. Sci. Rep. 5(1), 1–10 (2015). https://doi.org/10.1038/srep07684

    Article  Google Scholar 

  84. H.G. Liu, X.L. Liu, J.H. Yang, M.A.F. Sanjuán, G. Cheng, Detecting the weak high-frequency character signal by vibrational resonance in the duffing oscillator. Nonlinear Dyn. 89, 2621–2628 (2017). https://doi.org/10.1007/s11071-017-3610-2

    Article  MathSciNet  Google Scholar 

  85. Y. Xu, Y. Jia, M. Ge, L. Lu, L. Yang, X. Zhan, Effects of ion channel blocks on electrical activity of stochastic hodgkin-huxley neural network under electromagnetic induction. Neurocomputing 283, 196–204 (2018). https://doi.org/10.1016/j.neucom.2017.12.036

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61966022), the Natural Science Foundation Key Project of Gansu Province (No. 23JRRA860), the Natural Science Foundation of Gansu Province (No. 23JRRA913), and the key talent project of Gansu Province.

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  1. Kaijun Wu and Jiawei Li have contributed equally to this work.

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  1. School of Electronics and Information Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China

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All authors have contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Kaijun Wu and Jiawei Li. The first draft of the manuscript was written by Jiawei Li and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Wu, K., Li, J. Effects of high–low-frequency electromagnetic radiation on vibrational resonance in FitzHugh–Nagumo neuronal systems. Eur. Phys. J. B 96, 126 (2023). https://doi.org/10.1140/epjb/s10051-023-00594-z

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  • DOI: https://doi.org/10.1140/epjb/s10051-023-00594-z

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