Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

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Kulminskiy D. D., Ponomarenko V. I., Prokhorov M. D. Control of collective dynamics in multiplex networks of bistable time-delayed feedback oscillators with switched couplings. Izvestiya of Saratov University. Physics , 2022, vol. 22, iss. 4, pp. 310-319. DOI: 10.18500/1817-3020-2022-22-4-310-319, EDN: OARRCC

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2022
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Language: 
Russian
Heading: 
Radiophysics, electronics, acoustics
Article type: 
Article
UDC: 
537.86
DOI: 
10.18500/1817-3020-2022-22-4-310-319
EDN: 
OARRCC

Control of collective dynamics in multiplex networks of bistable time-delayed feedback oscillators with switched couplings

Autors: 
Kulminskiy Danil Dmitrievich, Saratov Branch of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences
Ponomarenko Vladimir Ivanovich, Saratov Branch of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences
Prokhorov Mikhail Dmitrievich, Saratov Branch of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences
Abstract: 

Background and Objectives: The study of complex collective dynamics in networks of coupled oscillators and its control is an important task for many scientific disciplines. Networks of nonlinear oscillators are capable of demonstrating a wide variety of spatiotemporal regimes of collective dynamics. One of these regimes is a chimera state that occurs in networks of identical oscillators and is characterized by the simultaneous existence in the network of both oscillators performing synchronous oscillations and oscillators with asynchronous behavior. The object of study in this paper is chimera states in multiplex networks consisting of three coupled rings, each of which consists of coupled identical bistable time-delay oscillators. Materials and Methods: The cases of unidirectional and mutual, time-varying couplings between rings (layers) of the network are considered. The control of collective dynamics, including chimera states in three-layer networks, was carried out by us in a radio physical experiment, in which radio engineering generators with time-delayed feedback were used as the node elements of the network. Each generator was a ring system consisting of a delay line, a nonlinear element, and a first-order low-frequency RC-filter. To implement the couplings between the network generators, an approach was used in which the couplings in the experimental setup are set programmatically. The control of chimera states in the network is implemented by an appropriate choice of initial conditions for bistable generators and by changing the topology of couplings between network layers. Results: It has been shown that at strong unidirectional coupling between the layers of the network, the chimera state is copied from layer to layer due to the synchronization of driven generators. At bidirectional coupling between the layers of the network, one can observe both the phenomenon of cloning of chimera states and the destruction of chimera states, depending on the choice of initial conditions for bistable generators. Conclusion: The obtained results are useful for better understanding the mechanisms of emergence of complex regimes of collective dynamics in multiplex networks with switched couplings.

Key words: 
multiplex networks
adaptive couplings
bistable oscillators
time-delay generators
chimera states
Acknowledgments: 
This study was supported by the Russian Science Foundation (project No. 22-22-00150, https://rscf.ru/en/project/22-22-00150/).
Reference: 
  1. Watts D. J. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton, Princeton University Press, 1999. 280 p.
  2. Strogatz S. H. Exploring complex networks. Nature, 2001, vol. 410, pp. 268–276. https://doi.org/10.1038/35065725
  3. Boccaletti S., Latora V., Moreno Y., Chavez M., Hwang D. Complex networks: Structure and dynamics. Phys. Rep., 2006, vol. 424, pp. 175–308. https://doi.org/10.1016/j.physrep.2005.10.009
  4. Osipov G. V., Kurths J., Zhou C. Synchronization in Oscillatory Networks. Berlin, Springer, 2007. 370 p.
  5. Abrams D. M., Strogatz S. H. Chimera states for coupled oscillators. Phys. Rev. Lett., 2004, vol. 93, article no. 174102. https://doi.org/10.1103/PhysRevLett.93.174102
  6. Parastesh F., Jafari S., Azarnoush H., Shahriari Z., Wang Z., Boccaletti S., Perc M. Chimeras. Phys. Rep., 2021, vol. 898, pp. 1–114. https://doi.org/10.1016/j.physrep.2020.10.003
  7. Hizanidis J., Kouvaris N. E., Zamora-López G., Díaz-Guilera A., Antonopoulos C. G. Chimera-like states in modular neural networks. Sci. Rep., 2016, vol. 6, article no. 19845. https://doi.org/10.1038/srep19845
  8. Maksimenko V. A., Makarov V. V., Bera B. K., Ghosh D., Dana S. K., Goremyko M. V., Frolov N. S., Koronovskii A. A., Hramov A. E. Excitation and suppression of chimera states by multiplexing. Phys. Rev. E, 2016, vol. 94, article no. 052205. https://doi.org/10.1103/PhysRevE.94.052205
  9. Andrzejak R. G., Ruzzene G., Malvestio I. Generalized synchronization between chimera states. Chaos, 2017, vol. 27, article no. 053114. https://doi.org/10.1063/1.4983841
  10. Majhi S., Perc M., Ghosh D. Chimera states in a multilayer network of coupled and uncoupled neurons. Chaos, 2017, vol. 27, article no. 073109. https://doi.org/10.1063/1.4993836
  11. Strelkova G. I., Vadivasova T. E., Anishchenko V. S. Synchronization of chimera states in a network of many unidirectionally coupled layers of discrete maps. Regul. Chaotic Dyn., 2018, vol. 23, pp. 948–960. https://doi.org/10.1134/S1560354718070092
  12. Sawicki J., Omelchenko I., Zakharova A., Schöll E. Synchronization scenarios of chimeras in multiplex networks. Eur. Phys. J. Spec. Top., 2018, vol. 227, pp. 1161–1171. https://doi.org/10.1140/epjst/e2018-800039-y
  13. Bukh A. V., Strelkova G. I., Anishchenko V. S. Synchronization of chimera states in coupled networks of nonlinear chaotic oscillators. Russ. J. Nonlinear Dyn., 2018, vol. 14, iss. 4, pp. 419–433 (in Russian).
  14. Rybalova E. V., Vadivasova T. E., Strelkova G. I., Anishchenko V. S., Zakharova A. S. Forced synchronization of a multilayer heterogeneous network of chaotic maps in the chimera state mode. Chaos, 2019, vol. 29, article no. 033134. https://doi.org/10.1063/1.5090184
  15. Bogatenko T. R., Bukh A. V., Anishchenko V. S., Strelkova G. I. Synchronization effects in a two-layer network of nonlocally coupled chaotic maps with dissipative and inertial intercoupling. Izvestiya of Saratov University. Physics, 2020, vol. 20, iss. 1, pp. 42–54 (in Russian). https://doi.org/10.18500/1817-3020-2020-20-1-42-54
  16. Shepherd G. M. The Synaptic Organization of the Brain. Oxford, Oxford University Press, 2004. 719 p.
  17. Maslennikov O. V., Nekorkin V. I. Adaptive dynamical networks. Physics-Uspekhi, 2017, vol. 60, pp. 694–704. https://doi.org/10.3367/UFNe.2016.10.037902
  18. Kasatkin D. V., Emelianova A. A., Nekorkin V. I. Nonlinear phenomena in Kuramoto networks with dynamical couplings. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, no. 4, pp. 635–675 (in Russian). https://doi.org/10.18500/0869-6632-2021-29-4-635-675
  19. Ponomarenko V. I., Kul’minskii D. D., Prokhorov M. D. An experimental study of synchronization of nonidentical neuronlike oscillators with an adaptive delayed coupling. Tech. Phys. Lett., 2018, vol. 44, pp. 761–764. https://doi.org/10.1134/S1063785018090109
  20. Nekorkin V. I., Kasatkin D. V., Dmitrichev A. S. Transient dynamics in a small ensemble of synaptically coupled Morris-Lecar neurons. Radiophys. Quantum Electron., 2010, vol. 53, pp. 45–52. https://doi.org/10.1007/s11141-010-9203-2
  21. Kasatkin D. V., Nekorkin V. I. Synchronization of chimera states in a multiplex system of phase oscillators with adaptive couplings. Chaos, 2018, vol. 28, article no. 093115. https://doi.org/10.1063/1.5031681
  22. Eser M. C., Medeiros E. S., Riza M., Zakharova A. Edges of inter-layer synchronization in multilayer networks with time-switching links. Chaos, 2021, vol. 31, article no. 103119. https://doi.org/10.1063/5.0065310
  23. Anwar M. S., Rakshit S., Ghosh D., Bollt E. M. Stability analysis of intralayer synchronization in time-varying multilayer networks with generic coupling functions. Phys. Rev. E, 2022, vol. 105, article no. 024303. https://doi.org/10.1103/PhysRevE.105.024303
  24. Dmitrichev A. S., Shchapin D. S., Nekorkin V. I. Cloning of chimera states in a multiplex network of two-frequency oscillators with linear local couplings. JETP Lett., 2018, vol. 108, pp. 543–547. https://doi.org/10.1134/S0021364018200079
  25. Dmitrichev A., Shchapin D., Nekorkin V. Cloning of chimera states in a large short-term coupled multiplex network of relaxation oscillators. Front. Appl. Math. Stat., 2019, vol. 5, article no. 9. https://doi.org/10.3389/fams.2019.00009
  26. Kulminskiy D. D., Ponomarenko V. I., Prokhorov M. D. Cloning of chimera states in a two-layer network of bistable time-delayed feedback oscillators. Tech. Phys. Lett., 2021, vol. 47, pp. 79–82. https://doi.org/10.1134/S1063785021010235
  27. Ponomarenko V. I., Kulminskiy D. D., Prokhorov M. D. Chimeralike states in networks of bistable time-delayed feedback oscillators coupled via the mean field. Phys. Rev. E, 2017, vol. 96, article no. 022209. https://doi.org/10.1103/PhysRevE.96.022209
  28. Kul’minskii D. D., Ponomarenko V. I., Sysoev I. V., Prokhorov M. D. A new approach to the experimental study of large ensembles of radioengineering oscillators with complex couplings. Tech. Phys. Lett., 2020, vol. 46, pp. 175–178. https://doi.org/10.1134/S1063785020020236
Received: 
16.06.2022
Accepted: 
30.08.2022
Published: 
30.11.2022
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