- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Self-organized bistability on scale-free networks

Nikita Frolov* and Alexander Hramov†

  • Center for Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad 236041, Russia and Institute of Information Technology, Mathematics and Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia

  • *phrolovns@gmail.com
  • †hramovae@gmail.com
PDF

Phys. Rev. E 106, 044301 – Published 10 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.044301

Abstract

A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states under the self-tuning of a control parameter. Many of these systems have a network organization that should be taken into account to understand the underlying processes in detail. In the present paper, we theoretically explore an extension of the SOB concept on the scale-free network under coupling constraints. As provided by the numerical simulations and mean-field approximation in the thermodynamic limit, SOB on scale-free networks originates from facilitated criticality reflected on both macro- and mesoscopic network scales. We establish that the appearance of switches is rooted in spatial self-organization and temporal self-similarity of the network's critical dynamics and replicates extreme properties of epileptic seizure recurrences. Our results, thus, indicate that the proposed conceptual model is suitable to deepen the understanding of emergent collective behavior behind neurological diseases.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. D. Angeli, J. E. Ferrell, and E. D. Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proc. Natl. Acad. Sci. USA 101, 1822 (2004).
  2. S. H. Strogatz, Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life (Hyperion, New York, 2012).
  3. A. N. Pisarchik and U. Feudel, Control of multistability, Phys. Rep. 540, 167 (2014).
  4. C. Koch, M. Massimini, M. Boly, and G. Tononi, Neural correlates of consciousness: Progress and problems, Nat. Rev. Neurosci. 17, 307 (2016).
  5. K. Linkenkaer-Hansen, V. V. Nikouline, J. M. Palva, and R. J. Ilmoniemi, Long-range temporal correlations and scaling behavior in human brain oscillations, J. Neurosci. 21, 1370 (2001).
  6. J. M. Beggs and D. Plenz, Neuronal avalanches in neocortical circuits, J. Neurosci. 23, 11167 (2003).
  7. P. Bak, How Nature Works: The Science of Self-Organized Criticality (Copernicus, New York, 1996).
  8. W. L. Shew and D. Plenz, The functional benefits of criticality in the cortex, Neuroscientist 19, 88 (2013).
  9. V. H. P. Louzada, N. A. M. Araújo, J. S. Andrade, Jr., and H. J. Herrmann, How to suppress undesired synchronization, Sci. Rep. 2, 658 (2012).
  10. K. Lehnertz, S. Bialonski, M.-T. Horstmann, D. Krug, A. Rothkegel, M. Staniek, and T. Wagner, Synchronization phenomena in human epileptic brain networks, J. Neurosci. Methods 183, 42 (2009).
  11. A. Lüttjohann and G. van Luijtelaar, Dynamics of networks during absence seizure's on- and offset in rodents and man, Front. Physiol. 6, 16 (2015).
  12. S. di Santo, R. Burioni, A. Vezzani, and M. A. Munoz, Self-Organized Bistability Associated with First-Order Phase Transitions, Phys. Rev. Lett. 116, 240601 (2016).
  13. D. Sornette and G. Ouillon, Dragon-kings: Mechanisms, statistical methods and empirical evidence, Eur. Phys. J.: Spec. Top. 205, 1 (2012).
  14. S. Kalitzin, G. Petkov, P. Suffczynski, V. Grigorovsky, B. L. Bardakjian, F. L. da Silva, and P. L. Carlen, Epilepsy as a manifestation of a multistate network of oscillatory systems, Neurobiology of Disease 130, 104488 (2019).
  15. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Complex networks: Structure and dynamics, Phys. Rep. 424, 175 (2006).
  16. S. Boccaletti, A. N. Pisarchik, C. I. Del Genio, and A. Amann, Synchronization: From Coupled Systems to Complex Networks (Cambridge University Press, Cambridge, UK, 2018).
  17. N. Frolov and A. Hramov, Extreme synchronization events in a kuramoto model: The interplay between resource constraints and explosive transitions, Chaos 31, 063103 (2021).
  18. R. Siracusa, R. Fusco, and S. Cuzzocrea, Astrocytes: role and functions in brain pathologies, Front. Pharmacol. 10, 1114 (2019).
  19. C. Diaz Verdugo, S. Myren-Svelstad, E. Aydin, E. Van Hoeymissen, C. Deneubourg, S. Vanderhaeghe, J. Vancraeynest, R. Pelgrims, M. I. Cosacak, A. Muto et al., Glia-neuron interactions underlie state transitions to generalized seizures, Nat. Commun. 10, 3830 (2019).
  20. J. Gómez-Gardeñes, S. Gómez, A. Arenas, and Y. Moreno, Explosive Synchronization Transitions in Scale-Free Networks, Phys. Rev. Lett. 106, 128701 (2011).
  21. B. C. Coutinho, A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Kuramoto model with frequency-degree correlations on complex networks, Phys. Rev. E 87, 032106 (2013).
  22. S. Boccaletti, J. Almendral, S. Guan, I. Leyva, Z. Liu, I. Sendiña-Nadal, Z. Wang, and Y. Zou, Explosive transitions in complex networks' structure and dynamics: Percolation and synchronization, Phys. Rep. 660, 1 (2016).
  23. A. Haimovici, E. Tagliazucchi, P. Balenzuela, and D. R. Chialvo, Brain Organization into Resting State Networks Emerges at Criticality on a Model of the Human Connectome, Phys. Rev. Lett. 110, 178101 (2013).
  24. M. T. Gastner and G. Ódor, The topology of large open connectome networks for the human brain, Sci. Rep. 6, 27249 (2016).
  25. A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286, 509 (1999).
  26. K.-I. Goh, B. Kahng, and D. Kim, Universal Behavior of Load Distribution in Scale-Free Networks, Phys. Rev. Lett. 87, 278701 (2001).
  27. F. Chung and L. Lu, Connected components in random graphs with given expected degree sequences, Ann. Combinat. 6, 125 (2002).
  28. T. Ichinomiya, Frequency synchronization in a random oscillator network, Phys. Rev. E 70, 026116 (2004).
  29. T. K. D.'M. Peron and F. A. Rodrigues, Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations, Phys. Rev. E 86, 056108 (2012).
  30. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Structure of Growing Networks with Preferential Linking, Phys. Rev. Lett. 85, 4633 (2000).
  31. P. L. Krapivsky, S. Redner, and F. Leyvraz, Connectivity of Growing Random Networks, Phys. Rev. Lett. 85, 4629 (2000).
  32. A. Mishra, S. Saha, M. Vigneshwaran, P. Pal, T. Kapitaniak, and S. K. Dana, Dragon-king-like extreme events in coupled bursting neurons, Phys. Rev. E 97, 062311 (2018).
  33. A. E. Hramov, A. A. Koronovskii, M. K. Kurovskaya, and S. Boccaletti, Ring Intermittency in Coupled Chaotic Oscillators at the Boundary of Phase Synchronization, Phys. Rev. Lett. 97, 114101 (2006).
  34. A. Hramov, A. A. Koronovskii, I. Midzyanovskaya, E. Sitnikova, and C. Van Rijn, On-off intermittency in time series of spontaneous paroxysmal activity in rats with genetic absence epilepsy, CHAOS 16, 043111 (2006).
  35. E. Sitnikova, A. E. Hramov, V. V. Grubov, A. A. Ovchinnkov, and A. A. Koronovsky, On–off intermittency of thalamo-cortical oscillations in the electroencephalogram of rats with genetic predisposition to absence epilepsy, Brain Res. 1436, 147 (2012).
  36. A. A. Koronovskii, A. E. Hramov, V. V. Grubov, O. I. Moskalenko, E. Sitnikova, and A. N. Pavlov, Coexistence of intermittencies in the neuronal network of the epileptic brain, Phys. Rev. E 93, 032220 (2016).
  37. N. S. Frolov, V. V. Grubov, V. A. Maksimenko, A. Lüttjohann, V. V. Makarov, A. N. Pavlov, E. Sitnikova, A. N. Pisarchik, J. Kurths, and A. E. Hramov, Statistical properties and predictability of extreme epileptic events, Sci. Rep. 9, 7243 (2019).
  38. A.-L. Barabási, Network science, Philos. Trans. R. Soc. A 371, 20120375 (2013).
  39. D. Fasino, A. Tonetto, and F. Tudisco, Generating large scale-free networks with the Chung–Lux random graph model, Networks 78, 174 (2021).

Outline

Information

Phys. Rev. E 106, 044301– Published 10 October, 2022
  • Received 25 March 2022
  • Revised 15 June 2022
  • Accepted 15 August 2022
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation