ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ramazanov I. R., Korneev I. A., Slepnev A. V., Vadivasova T. E. Synchronization of excitation waves in a two-layer network of FitzHugh–Nagumo neurons with noise modulation of interlayer coupling parameters. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, iss. 6, pp. 732-748. DOI: 10.18500/0869-6632-003016, EDN: FNRSUD

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
Full text PDF(En):
Article type: 
537.86; 519.21

Synchronization of excitation waves in a two-layer network of FitzHugh–Nagumo neurons with noise modulation of interlayer coupling parameters

Ramazanov Ibadulla Ramzesovich, Saratov State University
Korneev Ivan Aleksandrovich, Saratov State University
Slepnev Andrej Vjacheslavovich, Saratov State University
Vadivasova Tatjana Evgenevna, Saratov State University

The purpose of this work is to study the possibility of synchronization of wave processes in distributed excitable systems by means of noise modulation of the coupling strength between them. Methods. A simple model of a neural network, which consists of two coupled layers of excitable FitzHugh–Nagumo oscillators with a ring topology, is studied by numerical simulation methods. The connection between the layers has a random component, which is set for each pair of coupled oscillators by independent sources of colored Gaussian noise. Results. The possibility to obtain a regime close to full (in-phase) synchronization of traveling waves in the case of identical interacting layers and a regime of synchronization of wave propagation velocities in the case of non-identical layers differing in the values of the coefficients of intra-layer coupling is shown for certain values of parameters of coupling noise (intensity and correlation time). Conclusion. It is shown that the effects of synchronization of phases and propagation velocities of excitation waves in ensembles of neurons can be controlled using random processes of interaction of excitable oscillators set by statistically independent noise sources. In this case, both the noise intensity and its correlation time can serve as control parameters. The results obtained on a simple model can be quite general.

This work was supported by Russian Science Foundation, grant No. 20-12-00119
  1. Horsthemke W, Lefever R. Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology. Berlin, Heidelberg: Springer; 1984. 322 p. DOI: 10.1007/3-540-36852-3.
  2. Graham R. Macroscopic potentials, bifurcations and noise in dissipative systems. In: Garrido L, editor. Fluctuations and Stochastic Phenomena in Condensed Matter. Lecture Notes in Physics, vol. 268. Berlin, Heidelberg: Springer; 1987. P. 1–34. DOI: 10.1007/3-540-17206-8_1. 
  3. Schimansky-Geier L, Herzel H. Positive Lyapunov exponents in the Kramers oscillator. Journal of Statistical Physics. 1993;70(1–2):141–147. DOI: 10.1007/BF01053959.
  4. Arnold L. Random dynamical systems. In: Johnson R, editor. Dynamical Systems. Lecture Notes in Mathematics, vol. 1609. Berlin, Heidelberg: Springer; 1995. P. 1–43. DOI: 10.1007/BFb0095238.
  5. Moss F. Stochastic resonance: From the ice ages to the monkey’s ear. In: Weiss GH, editor. Contemporary Problems in Statistical Physics. Philadelphia, Pennsylvania: SIAM; 1994. P. 205–253. DOI: 10.1137/1.9781611971552.ch5.
  6. Kabashima S, Kawakubo T. Observation of a noise-induced phase transition in a parametric oscillator. Phys. Lett. A. 1979;70(5–6):375–376. DOI: 10.1016/0375-9601(79)90335-9.
  7. Pikovsky AS, Kurths J. Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 1997;78(5):775–778. DOI: 10.1103/PhysRevLett.78.775.
  8. Anishchenko VS, Neiman AB, Moss F, Shimansky-Geier L. Stochastic resonance: noise-enhanced order. Phys. Usp. 1999;42(1):7–36. DOI: 10.1070/PU1999v042n01ABEH000444.
  9. Bashkirtseva I, Ryashko L, Schurz H. Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances. Chaos, Solitons & Fractals. 2009;39(1):72–82. DOI: 10.1016/j.chaos.2007.01.128.
  10. Garcıa-Ojalvo J, Sancho JM. Noise in Spatially Extended Systems. New York: Springer; 1999. 307 p. DOI: 10.1007/978-1-4612-1536-3.
  11. Hou Z, Yang L, Xiaobin Z, Xin H. Noise induced pattern transition and spatiotemporal stochastic resonance. Phys. Rev. Lett. 1998;81(14):2854–2857. DOI: 10.1103/PhysRevLett.81.2854.
  12. Zimmermann MG, Toral R, Piro O, San Miguel M. Stochastic spatiotemporal intermittency and noise-induced transition to an absorbing phase. Phys. Rev. Lett. 2000;85(17):3612–3615. DOI: 10.1103/PhysRevLett.85.3612.
  13. Perc M. Noise-induced spatial periodicity in excitable chemical media. Chemical Physics Letters. 2005;410(1–3):49–53. DOI: 10.1016/j.cplett.2005.05.042.
  14. Cao FJ, Wood K, Lindenberg K. Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz. Phys. Rev. E. 2007;76(5):051111. DOI: 10.1103/PhysRevE. 76.051111.
  15. Slepnev AV, Shepelev IA, Vadivasova TE. Noise-induced effects in an active medium with periodic boundary conditions. Tech. Phys. Lett. 2014;40(1):62–64. DOI: 10.1134/S1063785014010271.
  16. Stratonovich RL. Selected Questions of the Theory of Fluctuations in Radio Engineering. Moscow: Sovetskoe Radio; 1961. 560 p. (in Russian).
  17. Neiman AB, Russell DF. Synchronization of noise-induced bursts in noncoupled sensory neurons. Phys. Rev. Lett. 2002;88(13):138103. DOI: 10.1103/PhysRevLett.88.138103.
  18. Ritt J. Evaluation of entrainment of a nonlinear neural oscillator to white noise. Phys. Rev. E. 2003;68(4):041915. DOI: 10.1103/PhysRevE.68.041915.
  19. Goldobin DS, Pikovsky A. Synchronization and desynchronization of self-sustained oscillators by common noise. Phys. Rev. E. 2005;71(4):045201. DOI: 10.1103/PhysRevE.71.045201.
  20. Hramov AE, Koronovskii AA, Moskalenko OI. Are generalized synchronization and noise-induced synchronization identical types of synchronous behavior of chaotic oscillators? Phys. Lett. A. 2006;354(5–6):423–427. DOI: 10.1016/j.physleta.2006.01.079.
  21. Nagai KH, Kori H. Noise-induced synchronization of a large population of globally coupled nonidentical oscillators. Phys. Rev. E. 2010;81(6):065202. DOI: 10.1103/PhysRevE.81.065202.
  22. Dolmatova AV, Goldobin DS, Pikovsky A. Synchronization of coupled active rotators by common noise. Phys. Rev. E. 2017;96(6):062204. DOI: 10.1103/PhysRevE.96.062204.
  23. Neiman A. Synchronizationlike phenomena in coupled stochastic bistable systems. Phys. Rev. E. 1994;49(4):3484–3487. DOI: 10.1103/PhysRevE.49.3484.
  24. Shulgin B, Neiman A, Anishchenko V. Mean switching frequency locking in stochastic bistable systems driven by a periodic force. Phys. Rev. Lett. 1995;75(23):4157–4160. DOI: 10.1103/ PhysRevLett.75.4157.
  25. Lindner JF, Meadows BK, Ditto WL, Inchiosa ME, Bulsara AR. Array enhanced stochastic resonance and spatiotemporal synchronization. Phys. Rev. Lett. 1995;75(1):3–6. DOI: 10.1103/ PhysRevLett.75.3.
  26. Anishchenko VS, Neiman AB. Stochastic synchronization. In: Schimansky-Geier L, Poschel T, editors. Stochastic Dynamics. Lecture Notes in Physics, vol. 484. Berlin, Heidelberg: Springer; 1997. P. 154–166. DOI: 10.1007/BFb0105607.
  27. Han SK, Yim TG, Postnov DE, Sosnovtseva OV. Interacting coherence resonance oscillators. Phys. Rev. Lett. 1999;83(9):1771–1774. DOI: 10.1103/PhysRevLett.83.1771.
  28. Neiman A, Schimansky-Geier L, Cornell-Bell A, Moss F. Noise-enhanced phase synchronization in excitable media. Phys. Rev. Lett. 1999;83(23):4896–4899. DOI: 10.1103/PhysRevLett.83.4896.
  29. Challenger JD, McKane AJ. Synchronization of stochastic oscillators in biochemical systems. Phys. Rev. E. 2013;88(1):012107. DOI: 10.1103/PhysRevE.88.012107.
  30. Semenova N, Zakharova A, Anishchenko V, Scholl E. Coherence-resonance chimeras in a network of excitable elements. Phys. Rev. Lett. 2016;117(1):014102.DOI: 10.1103/PhysRevLett.117.014102.
  31. Vadivasova TE, Slepnev AV, Zakharova A. Control of inter-layer synchronization by multiplexing noise. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2020;30(9):091101. DOI: 10.1063/ 5.0023071.
  32. Rybalova EV, Vadivasova TE, Strelkova GI, Zakharova A. Multiplexing noise induces synchronization in multilayer networks. Chaos, Solitons & Fractals. 2022;163:112521. DOI: 10.1016/j.chaos. 2022.112521.
  33. Nikishina NN, Rybalova EV, Strelkova GI, Vadivasova TE. Destruction of cluster structures in an ensemble of chaotic maps with noise-modulated nonlocal coupling. Regular and Chaotic Dynamics. 2022;27(2):242–251. DOI: 10.1134/S1560354722020083.
  34. Doiron B, Rinzel J, Reyes A. Stochastic synchronization in finite size spiking networks. Phys. Rev. E. 2006;74(3):030903. DOI: 10.1103/PhysRevE.74.030903.
  35. Patel A, Kosko B. Stochastic resonance in continuous and spiking neuron models with levy noise. IEEE Transactions on Neural Networks. 2008;19(12):1993–2008. DOI: 10.1109/TNN.2008.2005610.
  36. Ozer M, Perc M, Uzuntarla M. Stochastic resonance on Newman–Watts networks of Hodgkin– Huxley neurons with local periodic driving. Phys. Lett. A. 2009;373(10):964–968. DOI: 10.1016/ j.physleta.2009.01.034.
  37. He ZY, Zhou YR. Vibrational and stochastic resonance in the FitzHugh–Nagumo neural model with multiplicative and additive noise. Chinese Physics Letters. 2011;28(11):110505.DOI: 10.1088/0256- 307X/28/11/110505.
  38. Bressloff PC, Lai YM. Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. The Journal of Mathematical Neuroscience. 2011;1(1):2. DOI: 10.1186/2190- 8567-1-2.
  39. Kilpatrick ZP. Stochastic synchronization of neural activity waves. Phys. Rev. E. 2015;91(4):040701. DOI: 10.1103/PhysRevE.91.040701.
  40. Sharma SK, Malik MZ, Brojen Singh RK. Stochastic synchronization of neurons: the topologicalimpacts. Bioinformation. 2018;14(9):504–510. DOI: 10.6026/97320630014504.
  41. Yilmaz E, Ozer M, Baysal V, Perc M. Autapse-induced multiple coherence resonance in single neurons and neuronal networks. Scientific Reports. 2016;6(1):30914. DOI: 10.1038/srep30914.
  42. Yamakou ME, Jost J. Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network. Phys. Rev. E. 2019;100(2):022313. DOI: 10.1103/PhysRevE.100.022313.
  43. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal. 1961;1(6):445–466. DOI: 10.1016/S0006-3495(61)86902-6.
  44. Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon. Proceedings of the IRE. 1962;50(10):2061–2070. DOI: 10.1109/JRPROC.1962.288235.
Available online: