Skip to main content
SpringerLink
Log in

Conclusion and Outlook

  • Chapter
  • First Online:
Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Part of the book series: Springer Theses ((Springer Theses))

  • 296 Accesses

Abstract

Part I of this thesis was devoted to the analysis of cluster states in populations of globally coupled neurons with synaptic plasticity. Here, we used mathematical as well as numerical tools in order to understand the mechanism behind the emergence of frequency clustering. In Part II, we extended the findings of the first part towards more complex connectivity structures. For this, we extended the master stability approach to account for adaptive network structure and developed the multiplex decomposition method to study phase clusters on multiplex networks. In this chapter, we summarize all findings of this thesis and provide an outlook for future research.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Deco G, Jirsa VK, McIntosh AR, Sporns O, Kötter R (2009) Key role of coupling, delay, and noise in resting brain fluctuations. Proc Natl Acad Sci USA 106:10302

    Google Scholar 

  2. Ponce-Alvarez A, Deco G, Hagmann P, Romani GL, Mantini D, Corbetta M (2015) Resting-state temporal synchronization networks emerge from connectivity topology and heterogeneity. PLoS Comp Biol 11

    Google Scholar 

  3. Popovych OV, Xenakis MN, Tass PA (2015) The spacing principle for unlearning abnormal neuronal synchrony. PLoS ONE 10

    Google Scholar 

  4. Mantini D, Perrucci MG, Del Gratta C, Romani GL, Corbetta M (2007) Electrophysiological signatures of resting state networks in the human brain. Proc Natl Acad Sci USA 104:13170

    Google Scholar 

  5. Magri C, Schridde U, Murayama Y, Panzeri S (2012) The amplitude and timing of the bold signal reflects the relationship between local field potential power at different frequencies. J Neurosci 32:1395

    Google Scholar 

  6. Monto S, Palva S, Voipio J, Palva JM (2008) Very slow eeg fluctuations predict the dynamics of stimulus detection and oscillation amplitudes in humans. J Neurosci 28:8268

    Google Scholar 

  7. Alvarado-Rojas C, Valderrama M, Fouad-Ahmed A, Feldwisch-Drentrup H, Ihle M, Teixeira CA, Sales F, Schulze-Bonhage A, Adam C, Dourado A, Charpier S, Navarro V, Le Van Quyen M (2014) Slow modulations of high-frequency activity (40–140 Hz) discriminate preictal changes in human focal epilepsy. Sci Rep 4:4545

    Google Scholar 

  8. Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (2002) Model of thalamocortical slow-wave sleep oscillations and transitions to activated states. J Neurosci 22:8691

    Article  Google Scholar 

  9. Compte A, Sanchez-Vives MV, McCormick DA, Wang XJ (2003) Cellular and network mechanisms of slow oscillatory activity (\(<\)1 Hz) and wave propagations in a cortical network model. J Neurophys 89:2707

    Article  Google Scholar 

  10. Ashwin P, Burylko O (2015) Weak chimeras in minimal networks of coupled phase oscillators. Chaos 25

    Google Scholar 

  11. Bick C, Ashwin P (2016) Chaotic weak chimeras and their persistence in coupled populations of phase oscillators. Nonlinearity 29:1468

    Article  ADS  MathSciNet  Google Scholar 

  12. Calamai M, Politi A, Torcini A (2009) Stability of splay states in globally coupled rotators. Phys Rev E 80

    Google Scholar 

  13. Dipoppa M, Krupa M, Torcini A, Gutkin BS (2012) Splay states in finite pulse-coupled networks of excitable neurons. SIAM J Appl Dyn Syst 11:864

    Article  MathSciNet  Google Scholar 

  14. Fröhlich F (2016) Network neuroscience. Academic, Cambridge

    Google Scholar 

  15. Chakravartula S, Indic P, Sundaram B, Killingback T (2017) Emergence of local synchronization in neuronal networks with adaptive couplings. PLoS ONE 12

    Google Scholar 

  16. Kasatkin DV, Yanchuk S, Schöll E, Nekorkin VI (2017) Self-organized emergence of multi-layer structure and chimera states in dynamical networks with adaptive couplings. Phys Rev E 96

    Google Scholar 

  17. Jaros P, Brezetsky S, Levchenko R, Dudkowski D, Kapitaniak T, Maistrenko Y (2018) Solitary states for coupled oscillators with inertia. Chaos 28

    Google Scholar 

  18. Kruk N, Maistrenko Y, Koeppl H (2020) Solitary states in the mean-field limit. Chaos 30

    Google Scholar 

  19. Pecora LM, Carroll TL (1998) Master stability functions for synchronized coupled systems. Phys Rev Lett 80:2109

    Article  ADS  Google Scholar 

  20. Dahms T, Lehnert J, Schöll E (2012) Cluster and group synchronization in delay-coupled networks. Phys Rev E 86

    Google Scholar 

  21. Pecora LM, Sorrentino F, Hagerstrom AM, Murphy TE, Roy R (2014) Symmetries, cluster synchronization, and isolated desynchronization in complex networks. Nat Commun 5:4079

    Article  ADS  Google Scholar 

  22. Sorrentino F, Pecora LM, Hagerstrom AM, Murphy TE, Roy R (2016) Complete characterization of the stability of cluster synchronization in complex dynamical networks. Sci Adv 2

    Google Scholar 

  23. Sorrentino F, Ott E (2007) Network synchronization of groups. Phys Rev E 76

    Google Scholar 

  24. Choe CU, Dahms T, Hövel P, Schöll E (2010) Controlling synchrony by delay coupling in networks: from in-phase to splay and cluster states. Phys Rev E 81:025205(R)

    Article  ADS  Google Scholar 

  25. Flunkert V, Yanchuk S, Dahms T, Schöll E (2010) Synchronizing distant nodes: a universal classification of networks. Phys Rev Lett 105

    Google Scholar 

  26. Dahms T (2011) Synchronization in delay-coupled laser networks. Ph.D. thesis, Technische Universität Berlin

    Google Scholar 

  27. Heiligenthal S, Dahms T, Yanchuk S, Jüngling T, Flunkert V, Kanter I, Schöll E, Kinzel W (2011) Strong and weak chaos in nonlinear networks with time-delayed couplings. Phys Rev Lett 107

    Google Scholar 

  28. Kyrychko YN, Blyuss KB, Schöll E (2014) Synchronization of networks of oscillators with distributed-delay coupling. Chaos 24

    Google Scholar 

  29. Wille C, Lehnert J, Schöll E (2014) Synchronization-desynchronization transitions in complex networks: an interplay of distributed time delay and inhibitory nodes. Phys Rev E 90

    Google Scholar 

  30. Lehnert J (2016) Controlling synchronization patterns in complex networks, Springer Theses. Springer, Heidelberg

    Google Scholar 

  31. Belykh VN, Belykh IV, Hasler M (2004) Connection graph stability method for synchronized coupled chaotic systems. Phys D 195:159

    Article  MathSciNet  Google Scholar 

  32. Belykh IV, de Lange E, Hasler M (2005) Synchronization of bursting neurons: what matters in the network topology. Phys Rev Lett 94

    Google Scholar 

  33. Belykh IV, Belykh VN, Hasler M (2006) Generalized connection graph method for synchronization in asymmetrical networks. Phys D 224:42

    Article  MathSciNet  Google Scholar 

  34. Belykh IV, Belykh VN, Hasler M (2006) Synchronization in asymmetrically coupled networks with node balance. Chaos 16

    Google Scholar 

  35. Daley K, Zhao K, Belykh IV (2020) Synchronizability of directed networks: the power of non-existent ties. Chaos 30

    Google Scholar 

  36. Berner R, Vock S, Schöll E, Yanchuk S (2021) Desynchronization transitions in adaptive networks. Phys Rev Lett 126:028301

    Google Scholar 

  37. Vock S, Berner R, Yanchuk S, Schöll E (2021) Effect of diluted connectivities on cluster synchronization of adaptively coupled oscillator networks. arXiv:2101.05601

  38. Tass PA, Popovych OV (2012) Unlearning tinnitus-related cerebral synchrony with acoustic coordinated reset stimulation: theoretical concept and modelling. Biol Cybern 106:27

    Article  Google Scholar 

  39. Adamchic I, Hauptmann C, Barnikol UB, Pawelczyk N, Popovych OV, Barnikol TT, Silchenko AN, Volkmann J, Deuschl G, Meissner WG, Maarouf M, Sturm V, Freund HJ, Tass PA (2014) Coordinated reset neuromodulation for parkinson’s disease: proof-of-concept study. Movement Disord 29:1679

    Article  Google Scholar 

  40. Kromer JA, Tass PA (2020) Long-lasting desynchronization by decoupling stimulation. Phys Rev Research 2

    Google Scholar 

  41. Kromer JA, Khaledi-Nasab A, Tass PA (2020) Impact of number of stimulation sites on long-lasting desynchronization effects of coordinated reset stimulation. Chaos 30

    Google Scholar 

  42. Khaledi-Nasab A, Kromer JA, Tass PA (2021) Long-lasting desynchronization of plastic neural networks by random reset stimulation. Front Phys 11

    Google Scholar 

  43. Gómez S, Díaz-Guilera A, Gómez-Gardeñes J, Pérez Vicente CJ, Moreno Y, Arenas A (2013) Diffusion dynamics on multiplex networks. Phys Rev Lett 110:028701

    Google Scholar 

  44. Solé-Ribalta A, De Domenico M, Kouvaris NE, Díaz-Guilera A, Gómez S, Arenas A (2013) Spectral properties of the Laplacian of multiplex networks. Phys Rev E 88

    Google Scholar 

  45. Tang L, Wu X, Lü J, Lu J, D’Souza RM (2019) Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled rössler oscillators. Phys Rev E 99

    Google Scholar 

  46. Witthaut D, Rohden M, Zhang X, Hallerberg S, Timme M (2016) Critical links and nonlocal rerouting in complex supply networks. Phys Rev Lett 116

    Google Scholar 

  47. Totz CH, Olmi S, Schöll E (2020) Control of synchronization in two-layer power grids. Phys Rev E 102

    Google Scholar 

  48. Schäfer B, Witthaut D, Timme M, Latora V (2018) Dynamically induced cascading failures in power grids. Nat Commun 9:1975

    Article  ADS  Google Scholar 

  49. Olmi S (2015) Chimera states in coupled Kuramoto oscillators with inertia. Chaos 25

    Google Scholar 

  50. Mehrmann V, Morandin R, Olmi S, Schöll E (2018) Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form. Chaos 28

    Google Scholar 

  51. Tumash L, Olmi S, Schöll E (2018) Effect of disorder and noise in shaping the dynamics of power grids. Europhys Lett 123:20001

    Article  ADS  Google Scholar 

  52. Taher H, Olmi S, Schöll E (2019) Enhancing power grid synchronization and stability through time delayed feedback control. Phys Rev E 100

    Google Scholar 

  53. Tumash L, Zakharova A, Panteley E, Schöll E (2019) Synchronization patterns in Stuart-Landau networks: a reduced system approach. Eur Phys J B 92:100

    Article  ADS  MathSciNet  Google Scholar 

  54. Hellmann F, Schultz P, Jaros P, Levchenko R, Kapitaniak T, Kurths J, Maistrenko Y (2020) Network-induced multistability through lossy coupling and exotic solitary states. Nat Commun 11:592

    Article  ADS  Google Scholar 

  55. Berner R, Yanchuk S, Schöll E (2020) What adaptive neuronal networks teach us about power grids. Phys Rev E 103:042315

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Rico Berner

Authors
  1. Rico Berner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rico Berner .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Berner, R. (2021). Conclusion and Outlook. In: Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-74938-5_9

Download citation

Publish with us

Policies and ethics

Search

Navigation