Advertisement

Chimera states of neuron networks with adaptive coupling

  • Siyu Huo
  • Changhai Tian
  • Ling Kang
  • Zonghua LiuEmail author
Original Paper
  • 56 Downloads

Abstract

To better understand the diversity of dynamical patterns in the brain network of cerebral cortex, we study the collective behaviors of coupled neurons in complex networks with adaptive coupling. Based on the mutual interaction between dynamics and coupling strength in neuron systems, we let the coupling matrix evolve with the dynamics of neurons. We find that with suitable phase parameters, the coupling matrix will be self-organized into stabilized states and chimera states will be induced. The patterns of these chimera states may be different and abundant, depending on the different network topologies such as the fully connected, random, and scale-free networks. In particular, we apply this adaptive model to the realistic network of cerebral cortex and interestingly find that the adaptive coupling can also induce a diversity of chimera states, which may provide a new insight for the high capability of flexible brain functions. Moreover, we find that the preference of observing chimera states in heterogeneous networks is greater than that in homogeneous networks, and the latter is greater than that in the fully connected network, which may be one of the reasons for the nature to choose the specific sparse and heterogeneous structure of our brain network.

Keywords

Chimera state Adaptive coupling FitzHugh–Nagumo model Multi-clusters state Neuronal network 

Notes

Acknowledgements

This work was partially supported by the NNSF of China under Grant Nos. 11675056 and 11835003.

Compliance with ethical standards

Competing interest

The authors declare that they have no competing interests.

References

  1. 1.
    Acebron, J.A., Bonilla, L.L., Vicente, C.J.P., Ritort, F., Spigler, R.: The kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137 (2005)CrossRefGoogle Scholar
  2. 2.
    Boccaletti, S., Latora, V., Moreno, Y.: Complex networks: structure and dynamics. Phys. Rep. 424, 175 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469, 93 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Gomez-Gardenes, J., Gomez, S., Arenas, A., Moreno, Y.: Explosive synchronization transitions in scale-free networks. Phys. Rev. Lett. 106, 128701 (2011)CrossRefGoogle Scholar
  5. 5.
    Zhang, X., Hu, X., Kurths, J., Liu, Z.: Explosive synchronization in a general complex network. Phys. Rev. E 88, 010802(R) (2013)CrossRefGoogle Scholar
  6. 6.
    Zhang, X., Zou, Y., Boccaletti, S., Liu, Z.: Explosive synchronization as a process of explosive percolation in dynamical phase space. Sci. Rep. 4, 5200 (2014)CrossRefGoogle Scholar
  7. 7.
    Kim, M., Mashour, G.A., Moraes, S., Vanini, G., Tarnal, V., Janke, E., Hudetz, A.G., Lee, U.: Functional and topological conditions for explosive synchronization develop in human brain networks with the onset of anesthetic-induced unconsciousness. Front. Comput. Neurosci. 10, 1 (2016)CrossRefGoogle Scholar
  8. 8.
    Zhang, X., Boccaletti, S., Guan, S., Liu, Z.: Explosive synchronization in adaptive and multilayer networks. Phys. Rev. Lett. 114, 038701 (2015)CrossRefGoogle Scholar
  9. 9.
    Peron, T.K.D.M., Rodrigues, F.A.: Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations. Phys. Rev. E 86, 056108 (2012)CrossRefGoogle Scholar
  10. 10.
    Zou, Y., Pereira, T., Small, M., Liu, Z., Kurths, J.: Basin of attraction determines hysteresis in explosive synchronization. Phys. Rev. Lett. 112, 114102 (2014)CrossRefGoogle Scholar
  11. 11.
    Bi, H., Hu, X., Boccaletti, S., Wang, X., Zou, Y., Liu, Z., Guan, S.: Coexistence of quantized, time dependent, clusters in globally coupled oscillators. Phys. Rev. Lett. 117, 204101 (2016)CrossRefGoogle Scholar
  12. 12.
    Ji, P., Peron, T.K.D.M., Menck, P.J., Rodrigues, F.A., Kurths, J.: Cluster explosive synchronization in complex networks. Phys. Rev. Lett. 110, 218701 (2013)CrossRefGoogle Scholar
  13. 13.
    Kuramoto, Y., Battogtokh, D.: Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom. Complex Syst. 5, 380 (2002)Google Scholar
  14. 14.
    Sethia, G.C., Sen, A., Atay, F.M.: Clustered chimera states in delay-coupled oscillator systems. Phys. Rev. Lett. 100, 144102 (2008)CrossRefGoogle Scholar
  15. 15.
    Abrams, D.M., Strogatz, S.H.: Chimera states for coupled oscillators. Phys. Rev. Lett. 93, 174102 (2004)CrossRefGoogle Scholar
  16. 16.
    Omelchenko, E., Maistrenko, Y.L., Tass, P.A.: Chimera states: the natural link between coherence and incoherence. Phys. Rev. Lett. 100, 044105 (2008)CrossRefGoogle Scholar
  17. 17.
    Martens, E.A., Laing, C.R., Strogatz, S.H.: Solvable model of spiral wave chimeras. Phys. Rev. Lett. 104, 044101 (2010)CrossRefGoogle Scholar
  18. 18.
    Omelchenko, I., Provata, A., Hizanidis, J., Schöll, E., Hövel, P.: Robustness of chimera states for coupled Fitzhugh–Nagumo oscillators. Phys. Rev. E 91, 022917 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Boccaletti, S., Almendral, J.A., Guan, S., Leyva, I., Liu, Z., Sendiña-Nadal, I., Zou, Y.: Explosive transitions in complex networks structure and dynamics: percolation and synchronization. Phys. Rep. 660, 1 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Abrams, D.M., Mirollo, R., Strogatz, S.H., Wiley, D.A.: Solvable model for chimera states of coupled oscillators. Phys. Rev. Lett. 101, 084103 (2008)CrossRefGoogle Scholar
  21. 21.
    Sakaguchi, H.: Instability of synchronized motion in nonlocally coupled neural oscillators. Phys. Rev. E 73, 031907 (2006)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Pikovsky, A., Rosenblum, M.: Partially integrable dynamics of hierarchical populations of coupled oscillators. Phys. Rev. Lett. 101, 264103 (2008)CrossRefGoogle Scholar
  23. 23.
    Rattenborg, N.C., Amlaner, C.J., Lima, S.L.: Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neurosci. Biobehav. Rev. 24, 817 (2000)CrossRefGoogle Scholar
  24. 24.
    Mathews, C.G., Lesku, J.A., Lima, S.L., Amlaner, C.J.: Asynchronous eye closure as an anti-predator behavior in the western fence lizard. Ethology 112, 286 (2006)CrossRefGoogle Scholar
  25. 25.
    Ma, R., Wang, J., Liu, Z.: Robust features of chimera states and the implementation of alternating chimera states. Europhys. Lett. 91, 40006 (2010)CrossRefGoogle Scholar
  26. 26.
    Tamaki, M., Bang, J.W., Watanabe, T., Sasaki, Y.: Night watch in one brain hemisphere during sleep associated with the first-night effect in humans. Curr. Biol. 26, 1190 (2016)CrossRefGoogle Scholar
  27. 27.
    Omelchenko, I., Omel’chenko, E., Hövel, P., Schöll, E.: When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. Phys. Rev. Lett. 110, 224101 (2013)CrossRefGoogle Scholar
  28. 28.
    Hizanidis, J., Kanas, V.G., Bezerianos, A., Bountis, T.: Chimera states in networks of nonlocally coupled hindmarsh-rose neuron models. T. Int. J. Bifurc. Chaos 24, 1450030 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Olmi, S., Politi, A., Torcini, A.: Collective chaos in pulse-coupled neural networks. Europhys. Lett. 92, 60007 (2010)CrossRefGoogle Scholar
  30. 30.
    Santos, M.S., Szezech, J.D., Borges, F.S., Iarosz, K.C., Caldas, I.L., Batista, A.M., Viana, R.L., Kurths, J.: Chimera-like states in a neuronal network model of the cat brain. Chaos Solitons Fractals 101, 86 (2017)CrossRefGoogle Scholar
  31. 31.
    Hizanidis, J., Kouvaris, N.E., Zamora-Lopez, G., Diaz-Guilera, A., Antonopoulos, C.G.: Chimera-like states in modular neural networks. Sci. Rep. 6, 19845 (2016)CrossRefGoogle Scholar
  32. 32.
    Tian, C., Bi, H., Zhang, X., Guan, S., Liu, Z.: Asymmetric couplings enhance the transition from chimera state to synchronization. Phys. Rev. E 96, 052209 (2017)CrossRefGoogle Scholar
  33. 33.
    Tian, C., Zhang, X., Wang, Z., Liu, Z.: Diversity of chimera-like patterns from a model of 2D arrays of neurons with nonlocal coupling. Front. Phys. 12, 128904 (2017)CrossRefGoogle Scholar
  34. 34.
    Bi, G.Q., Poo, M.M.: Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J. Neurosci. 18, 10464 (1998)CrossRefGoogle Scholar
  35. 35.
    Markram, H., Lubke, J., Frotscher, M., Sakmann, B.: Regulation of synaptic efficacy by coincidence of postsynaptic aps and epsps. Science 275, 213 (1997)CrossRefGoogle Scholar
  36. 36.
    Caporale, N., Dan, Y.: Spike timing-dependent plasticity: a hebbian learning rule. Ann. Rev. Neurosci. 31, 25 (2008)CrossRefGoogle Scholar
  37. 37.
    Hebb, D.O.: The Organization of Behavior. Wiley, New York (1949)Google Scholar
  38. 38.
    Tero, A., et al.: Rules for biologically inspired adaptive network design. Science 327, 439 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Harris, K.D., et al.: Organization of cell assemblies in the hippocampus. Nature (London) 424, 552 (2003)CrossRefGoogle Scholar
  40. 40.
    Gross, T., Blasius, B.: Cascade dynamics of complex propagation. J. R. Soc. Interface 5, 259 (2008)CrossRefGoogle Scholar
  41. 41.
    Aoki, T., Aoyagi, T.: Self-organized network of phase oscillators coupled by activity-dependent interactions. Phys. Rev. E 84, 066109 (2011)CrossRefGoogle Scholar
  42. 42.
    Gutierrez, R., Amann, A., Assenza, S., Gomez-Gardenes, J., Latora, V., Boccaletti, S.: Emerging meso-and macroscales from synchronization of adaptive networks. Phys. Rev. Lett. 107, 234103 (2011)CrossRefGoogle Scholar
  43. 43.
    Aoki, T.: Self-organization of a recurrent network under ongoing synaptic plasticity. Neural Netw. 62, 11 (2015)CrossRefzbMATHGoogle Scholar
  44. 44.
    Kasatkin, D.V., Yanchuk, S., Scholl, E., Nekorkin, V.I.: Self-organized emergence of multilayer structure and chimera states in dynamical networks with adaptive couplings. Phys. Rev. E 96, 062211 (2017)CrossRefGoogle Scholar
  45. 45.
    Wang, H., Li, X.: Synchronization and chimera states of frequency-weighted Kuramoto-oscillator networks. Phys. Rev. E 83, 066214 (2011)CrossRefGoogle Scholar
  46. 46.
    Chandrasekar, V.K., Sheeba, J.H., Subash, B., Lakshmanan, M., Kurths, J.: Adaptive coupling induced multi-stable states in complex networks. Physica D 267, 36 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Kemeth, F.P., Haugland, S.W., Schmidt, L., Kevrekidis, I.G., Krischer, K.: A classification scheme for chimera states. Chaos 26, 094815 (2016)CrossRefGoogle Scholar
  48. 48.
    Zhu, Y., Zheng, Z., Yang, J.: Chimera states on complex networks. Phys. Rev. E 89, 022914 (2014)CrossRefGoogle Scholar
  49. 49.
    Albert, R., Barabasi, A.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Liu, Z., Lai, Y.C., Ye, N., Dasgupta, P.: Connectivity distribution and attack tolerance of general networks with both preferential and random attachments. Phys. Lett. A 303, 337 (2002)CrossRefzbMATHGoogle Scholar
  51. 51.
    Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C.J., Wedeen, J.V., Sporns, O.: Mapping the structural core of human cerebral cortex. PLoS Biol. 6, 1479 (2008)CrossRefGoogle Scholar
  52. 52.
    Honey, C.J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., Hagmann, P.: Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl. Acad. Sci. USA 106, 2035 (2009)CrossRefGoogle Scholar
  53. 53.
    Hong, H., Strogatz, S.H.: Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. Phys. Rev. Lett. 106, 054102 (2011)CrossRefGoogle Scholar
  54. 54.
    Borgers, C., Kopell, N.: Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural Comput. 15, 509 (2003)CrossRefzbMATHGoogle Scholar
  55. 55.
    Restrepo, J.G., Ott, E., Hunt, B.R.: Synchronization in large directed networks of coupled phase oscillators. Chaos 16, 015107 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Zhang, X., Guan, S., Zou, Y., Chen, X., Liu, Z.: Suppressing explosive synchronization by contrarians. Europhys. Lett. 113, 28005 (2016)CrossRefGoogle Scholar
  57. 57.
    Soriano, J., Martinez, M.R., Tlusty, T., Moses, E.: Development of input connections in neural cultures. Proc. Natl. Acad. Sci. USA 105, 13758 (2008)CrossRefGoogle Scholar
  58. 58.
    Vogels, T.P., Abbott, L.F.: Gating multiple signals through detailed balance of excitation and inhibition in spiking networks. Nat. Neurosci. 12, 483 (2009)CrossRefGoogle Scholar
  59. 59.
    Seliger, P., Young, S.C., Tsimring, L.S.: Plasticity and learning in a network of coupled phase oscillators. Phys. Rev. E 65, 041906 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  60. 60.
    Tang, J., Zhang, J., Ma, J., Luo, J.: Noise and delay sustained chimera state in small world neuronal network. Sci. China Technol. Sci. 61, (2018).  https://doi.org/10.1007/sl1431-017-9282-x
  61. 61.
    Liu, Z., Lai, Y.C.: Coherence resonance in coupled chaotic oscillators. Phys. Rev. Lett. 86, 4737 (2001)CrossRefGoogle Scholar
  62. 62.
    Zhan, M., Wei, G., Lai, C., Lai, Y.C., Liu, Z.: Coherence resonance near the hopf bifurcation in coupled chaotic oscillators. Phys. Rev. E 66, 036201 (2002)CrossRefGoogle Scholar
  63. 63.
    Zhu, L., Lai, Y.C., Liu, Z., Raghu, A.: Can noise make nonbursting chaotic systems more regular? Phys. Rev. E 66, 015204 (2002)CrossRefGoogle Scholar
  64. 64.
    Liu, Z., Lai, Y.C., Lopez, J.M.: Noise-induced enhancement of chemical reactions in chaotic flows. Chaos 12, 417 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsEast China Normal UniversityShanghaiChina
  2. 2.School of Data ScienceTongren UniversityTongrenChina

Personalised recommendations