Skip to main content

Advertisement

SpringerLink
Log in

Desynchronization and energy diversity between neurons

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Identical nonlinear oscillators can be regulated to present synchronous states, and non-identical oscillators are guided to reach phase lock when the coupling channels are controllable in physical way. Continuous energy supply and pumping are crucial for periodic or chaotic oscillators, and energy is exchanged when coupling channels are activated. Energy is pumped and accumulated with time during unidirectional coupling, and shape deformation can be induced in the media; as a result, parameter shifts occur. Continuous diffusion of intracellular and extracellular ions activates electromagnetic field in the biological neuron, and the inner field energy can be approached by equivalent Hamilton energy of neuron mapped from neural circuit. External energy injection and accommodation will induce local shape deformation and change in biophysical property, which can be described by parameters shift in the neuron model. In this paper, inner energy between synchronous neurons is pumped uniaxially and the coupling intensity is changed under energy diversity between neurons. To terminate continuous coupling and keep energy balance, shape deformation is induced accompanying possible shifts in some parameters. Therefore, the coupled identical neurons become non-identical with parameter mismatch, and complete synchronization is blocked. Under energy balance, the coupling intensity keeps a saturation value and parameter diversity is kept, and then, two non-identical neurons realized desynchronization. The results confirm that distinct energy diversity is important to realize desynchronization between neurons with parameters diversity and it is helpful to prevent the occurrence of seizure accompanied with synchronous bursting in neurons.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Data availability

The datasets generated and/or analyzed in this work are available upon request from the corresponding author.

References

  1. Wang, Y., Wang, C., Ren, G., et al.: Energy dependence on modes of electric activities of neuron driven by multi-channel signals. Nonlinear Dyn. 89, 1967–1987 (2017)

    Google Scholar 

  2. Usha, K., Subha, P.A.: Collective dynamics and energy aspects of star-coupled Hindmarsh-Rose neuron model with electrical, chemical and field couplings. Nonlinear Dyn. 96, 2115–2124 (2019)

    MATH  Google Scholar 

  3. Usha, K., Subha, P.A.: Energy feedback and synchronous dynamics of Hindmarsh-Rose neuron model with memristor. Chin. Phys. B 28, 020502 (2019)

    Google Scholar 

  4. Yang, Y., Ma, J., Xu, Y., et al.: Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction. Cogn. Neurodyn. 15, 265–277 (2021)

    Google Scholar 

  5. Njitacke, Z.T., Fozin, T.F., Muni, S.S., et al.: Energy computation, infinitely coexisting patterns and their control from a Hindmarsh-Rose neuron with memristiveautapse: circuit implementation. AEU Int. J. Electron. Commun. 155, 154361 (2022)

    Google Scholar 

  6. Groschner, L.N., Malis, J.G., Zuidinga, B., et al.: A biophysical account of multiplication by a single neuron. Nature 603, 119–123 (2022)

    Google Scholar 

  7. Wu, F., Ma, J., Zhang, G.: Energy estimation and coupling synchronization between biophysical neurons. Sci. China Technol. Sci. 63, 625–636 (2020)

    Google Scholar 

  8. Nagel, K.I., Wilson, R.I.: Biophysical mechanisms underlying olfactory receptor neuron dynamics. Nat. Neurosci. 14, 208–216 (2011)

    Google Scholar 

  9. Gjorgjieva, J., Drion, G., Marder, E.: Computational implications of biophysical diversity and multiple timescales in neurons and synapses for circuit performance. Curr. Opin. Neurobiol. 37, 44–52 (2016)

    Google Scholar 

  10. Ye, J., Rozdeba, P.J., Morone, U.I., et al.: Estimating the biophysical properties of neurons with intracellular calcium dynamics. Phys. Rev. E 89, 062714 (2014)

    Google Scholar 

  11. Lotter, W., Kreiman, G., Cox, D.: A neural network trained for prediction mimics diverse features of biological neurons and perception. Nat. Mach. Intell. 2, 210–219 (2020)

    Google Scholar 

  12. Szücs, A., Varona, P., Volkovskii, A.R., et al.: Interacting biological and electronic neurons generate realistic oscillatory rhythms. NeuroReport 11, 563–569 (2000)

    Google Scholar 

  13. Montani, F., Baravalle, R., Montangie, L., et al.: Causal information quantification of prominent dynamical features of biological neurons. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 373, 20150109 (2015)

    MathSciNet  MATH  Google Scholar 

  14. Carta, G., Gambarotta, G., Fornasari, B.E., et al.: The neurodynamic treatment induces biological changes in sensory and motor neurons in vitro. Sci. Rep. 11, 13277 (2021)

    Google Scholar 

  15. Newman, J.P., Butera, R.J.: Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons. Chaos 20, 023118 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Wu, F., Hu, X., Ma, J.: Estimation of the effect of magnetic field on a memristive neuron. Appl. Math. Comput. 432, 127366 (2022)

    MathSciNet  MATH  Google Scholar 

  17. Ignatov, M., Ziegler, M., Hansen, M., et al.: A memristive spiking neuron with firing rate coding. Front. Neurosci. 9, 376 (2015)

    Google Scholar 

  18. Yang, R., Huang, H.M., Guo, X.: Memristive synapses and neurons for bioinspired computing. Adv. Electron. Mater. 5, 1900287 (2019)

    Google Scholar 

  19. Lai, Q., Lai, C., Zhang, H., et al.: Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption. Chaos Solitons Fractals 158, 112017 (2022)

    MathSciNet  Google Scholar 

  20. Bao, H., Hua, Z.Y., Liu, W.B., et al.: Discrete memristive neuron model and its interspike interval-encoded application in image encryption. Sci. China Technol. Sci. 64, 2281–2291 (2021)

    Google Scholar 

  21. Lin, H., Wang, C., Deng, Q., et al.: Review on chaotic dynamics of memristive neuron and neural network. Nonlinear Dyn. 106, 959–973 (2021)

    Google Scholar 

  22. Guo, Y., Zhu, Z., Wang, C., et al.: Coupling synchronization between photoelectric neurons by using memristive synapse. Optik 218, 164993 (2020)

    Google Scholar 

  23. Xu, Y., Liu, M., Zhu, Z., et al.: Dynamics and coherence resonance in a thermosensitive neuron driven by photocurrent. Chin. Phys. B 29, 098704 (2020)

    Google Scholar 

  24. Yao, Z., Wang, C.: Collective behaviors in a multiple functional network with hybrid synapses. Physica A 605, 127981 (2022)

    MATH  Google Scholar 

  25. Hussain, I., Jafari, S., Ghosh, D., et al.: Synchronization and chimeras in a network of photosensitive FitzHugh–Nagumo neurons. Nonlinear Dyn. 104, 2711–2721 (2021)

    Google Scholar 

  26. Marino, A., Genchi, G.G., Sinibaldi, E., et al.: Piezoelectric effects of materials on bio-interfaces. ACS Appl. Mater. Interfaces. 9, 17663–17680 (2017)

    Google Scholar 

  27. Zhang, X., Cui, X., Wang, D., et al.: Piezoelectric nanotopography induced neuron-like differentiation of stem cells. Adv. Func. Mater. 29, 1900372 (2019)

    Google Scholar 

  28. Rajabi, A.H., Jaffe, M., Arinzeh, T.L.: Piezoelectric materials for tissue regeneration: a review. Acta Biomater. 24, 12–23 (2015)

    Google Scholar 

  29. Njitacke, Z.T., Doubla, I.S., Kengne, J., et al.: Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse. Chaos 30, 023101 (2020)

    MathSciNet  MATH  Google Scholar 

  30. Alcamí, P., Pereda, A.E.: Beyond plasticity: the dynamic impact of electrical synapses on neural circuits. Nat. Rev. Neurosci. 20, 253–271 (2019)

    Google Scholar 

  31. Kuo, S.P., Schwartz, G.W., Rieke, F.: Nonlinear spatiotemporal integration by electrical and chemical synapses in the retina. Neuron 90, 320–332 (2016)

    Google Scholar 

  32. Ge, P., Cao, H.: Synchronization of Rulkov neuron networks coupled by excitatory and inhibitory chemical synapses. Chaos 29, 023129 (2019)

    MathSciNet  MATH  Google Scholar 

  33. Xu, Y., Jia, Y., Wang, H., et al.: Spiking activities in chain neural network driven by channel noise with field coupling. Nonlinear Dyn. 95, 3237–3247 (2019)

    MATH  Google Scholar 

  34. Guo, Y., Wang, C., Yao, Z., et al.: Desynchronization of thermosensitive neurons by using energy pumping. Physica A 602, 127644 (2022)

    MathSciNet  MATH  Google Scholar 

  35. Zhou, Q., Wei, D.Q.: Collective dynamics of neuronal network under synapse and field coupling. Nonlinear Dyn. 105, 753–765 (2021)

    Google Scholar 

  36. Sarasola, C., Torrealdea, F.J., d’Anjou, A., et al.: Energy balance in feedback synchronization of chaotic systems. Phys. Rev. E 69, 011606 (2004)

    Google Scholar 

  37. Hou, Y., Fang, P.: Synchronization and stability of two unbalanced rotors with fast antirotation considering energy balance. Math. Probl. Eng. 2015, 694145 (2015)

    MathSciNet  MATH  Google Scholar 

  38. Torrealdea, F.J., d’Anjou, A., Graña, M., et al.: Energy aspects of the synchronization of model neurons. Phys. Rev. E 74, 011905 (2006)

    Google Scholar 

  39. Koluda, P., Perlikowski, P., Czolczynski, K., et al.: Synchronization configurations of two coupled double pendula. Commun. Nonlinear Sci. Numer. Simul. 19, 977–990 (2014)

    MathSciNet  MATH  Google Scholar 

  40. Yao, Z., Zhou, P., Alsaedi, A., et al.: Energy flow-guided synchronization between chaotic circuits. Appl. Math. Comput. 374, 124998 (2020)

    MathSciNet  MATH  Google Scholar 

  41. Zhang, X., Yao, Z., Guo, Y., et al.: Target wave in the network coupled by thermistors. Chaos Solitons Fractals 142, 110455 (2021)

    MathSciNet  Google Scholar 

  42. Zhang, X., Wang, C., Ma, J., et al.: Control and synchronization in nonlinear circuits by using a thermistor. Mod. Phys. Lett. B 34, 2050267 (2020)

    MathSciNet  Google Scholar 

  43. Fossi, J.T., Deli, V., Edima, H.C., et al.: Phase synchronization between two thermo-photoelectric neurons coupled through a Josephson Junction. Eur. Phys. J. B 95, 66 (2022)

    Google Scholar 

  44. Zhang, X., Ma, J., Xu, Y., et al.: Synchronization between FitzHugh-Nagumo neurons coupled with phototube. Acta Phys. Sin. 70, 090502 (2021)

    Google Scholar 

  45. Huang, P., Guo, Y., Ren, G., et al.: Energy-induced resonance synchronization in neural circuits. Mod. Phys. Lett. B 35, 2150433 (2021)

    MathSciNet  Google Scholar 

  46. Zhang, Y., Zhou, P., Yao, Z., et al.: Resonance synchronisation between memristive oscillators and network without variable coupling. Pramana J Phys 95, 49 (2021)

    Google Scholar 

  47. Garcia-Alvarez, D., Bahraminasab, A., Stefanovska, A., et al.: Competition between noise and coupling in the induction of synchronisation. EPL 88, 30005 (2009)

    Google Scholar 

  48. Ambika, G., Menon, K., Harikrishnan, K.P.: Noise induced resonance phenomena in coupled map lattices. Eur. Phys. J. B Condens. Matter Complex Syst. 49, 225–230 (2006)

    Google Scholar 

  49. He, D., Shi, P., Stone, L.: Noise-induced synchronization in realistic models. Phys. Rev. E 67, 027201 (2003)

    Google Scholar 

  50. Toral, R., Mirasso, C.R., Hernández-Garcıa, E., et al.: Analytical and numerical studies of noise-induced synchronization of chaotic systems. Chaos 11, 665–673 (2001)

    MATH  Google Scholar 

  51. Muni, S.S., Fatoyinbo, H.O., Ghosh, I.: Dynamical effects of electromagnetic flux on chialvo neuron map: nodal and network behaviors. Int. J. Bifurc. Chaos 32, 2230020 (2022)

    MathSciNet  MATH  Google Scholar 

  52. Muni, S.S., Rajagopal, K., Karthikeyan, A., et al.: Discrete hybrid Izhikevich neuron model: nodal and network behaviours considering electromagnetic flux coupling. Chaos Solitons Fractals 155, 111759 (2022)

    Google Scholar 

  53. Yuan, Z., Feng, P., Fan, Y., et al.: Astrocytic modulation on neuronal electric mode selection induced by magnetic field effect. Cogn. Neurodyn. 16, 183–194 (2022)

    Google Scholar 

  54. Kyprianidis, I.M., Papachristou, V., Stouboulos, I.N., et al.: Dynamics of coupled chaotic Bonhoeffer-van der Pol Oscillators. WSEAS Trans. Syst. 11, 516–526 (2012)

    Google Scholar 

  55. Zhang, X., Ma, J.: Wave filtering and firing modes in a light-sensitive neural circuit. J. Zhejiang Univ. Sci. A 22, 707–720 (2021)

    Google Scholar 

  56. Xie, Y., Yao, Z., Hu, X., et al.: Enhance sensitivity to illumination and synchronization in light-dependent neurons. Chin. Phys. B 30, 120510 (2021)

    Google Scholar 

  57. Liu, Y., Xu, W., Ma, J., et al.: A new photosensitive neuron model and its dynamics. Front. Inf. Technol. Electron. Eng. 21, 1387–1396 (2020)

    Google Scholar 

  58. Guo, Y., Zhou, P., Yao, Z., et al.: Biophysical mechanism of signal encoding in an auditory neuron. Nonlinear Dyn. 105, 3603–3614 (2021)

    Google Scholar 

  59. Zhou, P., Yao, Z., Ma, J., et al.: A piezoelectric sensing neuron and resonance synchronization between auditory neurons under stimulus. Chaos Solitons Fractals 145, 110751 (2021)

    MathSciNet  Google Scholar 

  60. Zhang, Y., Wang, C.N., Tang, J., et al.: Phase coupling synchronization of FHN neurons connected by a Josephson junction. Sci. China Technol. Sci. 63, 2328–2338 (2020)

    Google Scholar 

  61. Crotty, P., Schult, D., Segall, K.: Josephson junction simulation of neurons. Phys. Rev. E 82, 011914 (2010)

    Google Scholar 

  62. Zhang, Y., Zhou, P., Tang, J., et al.: Mode selection in a neuron driven by Josephson junction current in presence of magnetic field. Chin. J. Phys. 71, 72–84 (2021)

    MathSciNet  Google Scholar 

  63. Zhang, Y., Xu, Y., Yao, Z., et al.: A feasible neuron for estimating the magnetic field effect. Nonlinear Dyn. 102, 1849–1867 (2020)

    Google Scholar 

  64. Xie, Y., Yao, Z., Ma, J.: Phase synchronization and energy balance between neurons. Front. Inf. Technol. Electron. Eng. 23, 1407–1420 (2022)

    Google Scholar 

  65. Wang, Y., Sun, G., Ren, G.: Diffusive field coupling induced synchronization between neural circuits under energy balance. Chin. Phys. B 32, 040504 (2023)

    Google Scholar 

  66. Wang, C., Sun, G., Yang, F., et al.: Capacitive coupling memristive systems for energy balance. AEU Int. J. Electron. Commun. 153, 154280 (2022)

    Google Scholar 

  67. Zhou, P., Zhang, X., Ma, J.: How to wake up the electric synapse coupling between neurons? Nonlinear Dyn. 108, 1681–1695 (2022)

    Google Scholar 

  68. Ma, X., Xu, Y.: Taming the hybrid synapse under energy balance between neurons. Chaos Solitons Fractals 159, 112149 (2022)

    MathSciNet  Google Scholar 

  69. Xie, Y., Yao, Z., Ma, J.: Formation of local heterogeneity under energy collection in neural networks. Sci. China Technol. Sci. 66, 439–455 (2023)

    Google Scholar 

  70. Ma, J.: Biophysical neurons, energy, and synapse controllability: a review. J. Zhejiang Univ. Sci. A 24, 109–129 (2023)

    Google Scholar 

Download references

Funding

This project is partially supported by National Natural Science Foundation of China under Grant No. 12072139.

Author information

Authors and Affiliations

  1. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Ying Xie & Jun Ma

  2. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Ying Xu

  3. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 430065, China

    Jun Ma

Authors
  1. Ying Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Ma.

Ethics declarations

Conflict of interest

The authors confirm no conflict of interest with publication of this work.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xie, Y., Xu, Y. & Ma, J. Desynchronization and energy diversity between neurons. Nonlinear Dyn 111, 11521–11541 (2023). https://doi.org/10.1007/s11071-023-08468-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08468-w

Keywords

Search

Navigation