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Noise and delay sustained chimera state in small world neuronal network

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Abstract

Chimera state in neuronal network means the coexistence of synchronized and desynchronized firing patterns. It attracts much attention recently due to its possible relevance to the phenomenon of unihemispheric sleep in mammals. In this paper, we search for chimera state in a noisy small-world neuronal network, in which the neurons are delayed coupled. We found both transient and permanent chimera state when time delay is close to a critical value. The chimera state occurs due to the competition between the synchronized and desynchronized patterns in the neuronal network. On the other hand, intermediate intensity of noise facilitates the occurrence of delay-sustained chimera states. Comparison between noise and delay shows that time delay is the key factor determining the chimera state, whereas noise is a subordinate one.

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References

  1. Kuramoto Y, Battogtokh D. Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom Complex Syst, 2002, 5: 380–385

    Google Scholar 

  2. Zhang X, Bi H, Guan S, et al. Model bridging chimera state and explosive synchronization. Phys Rev E, 2016, 94: 012204

    Article  Google Scholar 

  3. Singha J, Gupte N. Spatial splay states and splay chimera states in coupled map lattices. Phys Rev E, 2016, 94: 052204

    Article  Google Scholar 

  4. Maksimenko V A, Makarov V V, Bera B K, et al. Excitation and suppression of chimera states by multiplexing. Phys Rev E, 2016, 94: 052205

    Article  Google Scholar 

  5. Abrams D M, Strogatz S H. Chimera states for coupled oscillators. Phys Rev Lett, 2004, 93: 174102

    Article  Google Scholar 

  6. Abrams D M, Mirollo R, Strogatz S H, et al. Solvable model for Chimera states of coupled oscillators. Phys Rev Lett, 2008, 101: 084103

    Article  Google Scholar 

  7. Laing C R. The dynamics of chimera states in heterogeneous Kuramoto networks. Phys D-Nonlinear Phenomena, 2009, 238: 1569–1588

    Article  MathSciNet  MATH  Google Scholar 

  8. Martens E A, Laing C R, Strogatz S H. Solvable model of spiral wave chimeras. Phys Rev Lett, 2010, 104: 044101

    Article  Google Scholar 

  9. Omel’chenko O E, Wolfrum M, Yanchuk S, et al. Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally- coupled phase oscillators. Phys Rev E, 2012, 85: 036210

    Article  Google Scholar 

  10. Martens E A. Chimeras in a network of three oscillator populations with varying network topology. Chaos, 2010, 20: 043122

    Article  MathSciNet  MATH  Google Scholar 

  11. Wolfrum M, Omel’chenko O E, Yanchuk S, et al. Spectral properties of chimera states. Chaos, 2011, 21: 013112

    Article  MathSciNet  MATH  Google Scholar 

  12. Maistrenko Y, Brezetsky S, Jaros P, et al. Smallest chimera states. Phys Rev E, 2017, 95: 010203

    Article  Google Scholar 

  13. Premalatha K, Chandrasekar V K, Senthilvelan M, et al. Chimeralike states in two distinct groups of identical populations of coupled Stuart-Landau oscillators. Phys Rev E, 2017, 95: 022208

    Article  MathSciNet  Google Scholar 

  14. Mishra A, Saha S, Hens C, et al. Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a Josephson junction array. Phys Rev E, 2017, 95: 010201

    Article  Google Scholar 

  15. Omel’chenko O E, Wolfrum M, Maistrenko Y L. Chimera states as chaotic spatiotemporal patterns. Phys Rev E, 2010, 81: 065201

    Article  MathSciNet  Google Scholar 

  16. Cano A V, Cosenza M G. Chimeras and clusters in networks of hyperbolic chaotic oscillators. Phys Rev E, 2017, 95: 030202

    Article  MathSciNet  Google Scholar 

  17. Ujjwal S R, Punetha N, Prasad A, et al. Emergence of chimeras through induced multistability. Phys Rev E, 2017, 95: 032203

    Article  Google Scholar 

  18. Schmidt A, Kasimatis T, Hizanidis J, et al. Chimera patterns in twodimensional networks of coupled neurons. Phys Rev E, 2017, 95: 032224

    Article  MathSciNet  Google Scholar 

  19. Omelchenko I, Omel’Chenko O E, Hövel P, et al. When nonlocal coupling between oscillators becomes stronger: Patched synchrony or multichimera states. Phys Rev Lett, 2013, 110: 224101

    Article  Google Scholar 

  20. Laing C R, Chow C C. Stationary bumps in networks of spiking neurons. Neural Comput, 2001, 13: 1473–1494

    Article  MATH  Google Scholar 

  21. Sakaguchi H. Instability of synchronized motion in nonlocally coupled neural oscillators. Phys Rev E, 2006, 73: 031907

    Article  MathSciNet  Google Scholar 

  22. Martens E A, Thutupalli S, Fourrière A, et al. Chimera states in mechanical oscillator networks. Proc Natl Acad Sci USA, 2013, 110: 10563–10567

    Article  Google Scholar 

  23. Hagerstrom A M, Murphy T E, Roy R, et al. Experimental observation of chimeras in coupled-map lattices. Nat Phys, 2012, 8: 658–661

    Article  Google Scholar 

  24. Tinsley M R, Nkomo S, Showalter K. Chimera and phase-cluster states in populations of coupled chemical oscillators. Nat Phys, 2012, 8: 662–665

    Article  Google Scholar 

  25. Larger L, Penkovsky B, Maistrenko Y. Virtual chimera states for delayed-feedback systems. Phys Rev Lett, 2013, 111: 054103

    Article  Google Scholar 

  26. Isomura Y, Fujiwara-Tsukamoto Y, Takada M. A network mechanism underlying hippocampal seizure-like synchronous oscillations. NeuroSci Res, 2008, 61: 227–233

    Article  Google Scholar 

  27. Tass P A, Qin L, Hauptmann C, et al. Coordinated reset has sustained aftereffects in Parkinsonian monkeys. Ann Neurol, 2012, 72: 816–820

    Article  Google Scholar 

  28. Rattenborg N C, Amlaner C J, Lima S L. Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. NeuroSci BioBehaval Rev, 2000, 24: 817–842

    Article  Google Scholar 

  29. Rial R, González J, Gené L, et al. Asymmetric sleep in apneic human patients. Am J Physiol-Regulatory Integrative Comp Physiol, 2013, 304: R232–R237

    Article  Google Scholar 

  30. Omel’chenko O E. Coherence-incoherence patterns in a ring of nonlocally coupled phase oscillators. Nonlinearity, 2013, 26: 2469–2498

    Article  MathSciNet  MATH  Google Scholar 

  31. Glaze T A, Lewis S, Bahar S. Chimera states in a Hodgkin-Huxley model of thermally sensitive neurons. Chaos, 2016, 26: 083119

    Article  MathSciNet  Google Scholar 

  32. Laing C R. Chimeras in networks of planar oscillators. Phys Rev E, 2010, 81: 066221

    Article  MathSciNet  Google Scholar 

  33. Shanahan M. Metastable chimera states in community-structured oscillator networks. Chaos, 2010, 20: 013108

    Article  MathSciNet  Google Scholar 

  34. Zhu Y, Zheng Z, Yang J. Chimera states on complex networks. Phys Rev E, 2014, 89: 022914

    Article  Google Scholar 

  35. Yeldesbay A, Pikovsky A, Rosenblum M. Chimeralike states in an ensemble of globally coupled oscillators. Phys Rev Lett, 2014, 112: 144103

    Article  Google Scholar 

  36. Omelchenko I, Provata A, Hizanidis J, et al. Robustness of chimera states for coupled FitzHugh-Nagumo oscillators. Phys Rev E, 2015, 91: 022917

    Article  MathSciNet  Google Scholar 

  37. Kandel E R, Schwartz J H, Jessell T M. Principles of Neural Science. Amsterdam: Elsevier, 1991

    Google Scholar 

  38. Wang Q, Perc M, Duan Z, et al. Synchronization transitions on scalefree neuronal networks due to finite information transmission delays. Phys Rev E, 2009, 80: 026206

    Article  Google Scholar 

  39. Yu W T, Tang J, Ma J, et al. Heterogeneous delay-induced asynchrony and resonance in a small-world neuronal network system. EPL, 2016, 114: 50006

    Article  Google Scholar 

  40. Qian Y, Zhang Z. Effects of time delay and connection probability on self-sustained oscillations and synchronization transitions in excitable Erdös-Rényi random networks. Commun Nonlinear Sci Numer Simul, 2017, 47: 127–138

    Article  MathSciNet  Google Scholar 

  41. Sun X, Perc M, Kurths J. Effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks. Chaos, 2017, 27: 053113

    Article  MathSciNet  Google Scholar 

  42. Zheng Y G, Bao L J. Effect of topological structure on synchronizability of network with connection delay. Chaos Solitons Fractals, 2017, 98: 145–151

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhu J, Liu X. Locking induced by distance-dependent delay in neuronal networks. Phys Rev E, 2016, 94: 052405

    Article  Google Scholar 

  44. Yang X L, Hu L P, Sun Z K. How time-delayed coupling influences differential feedback control of bursting synchronization in modular neuronal network. Nonlinear Dyn, 2016, 86: 1797–1806

    Article  Google Scholar 

  45. Qian Y. Time delay and long-range connection induced synchronization transitions in Newman-Watts small-world neuronal networks. PLoS ONE, 2014, 9: e96415

    Article  Google Scholar 

  46. Fan D G, Wang Q Y. Synchronization and bursting transition of the coupled Hindmarsh-Rose systems with asymmetrical time-delays. Sci China Technol Sci, 2017, 60: 1019–1031

    Article  Google Scholar 

  47. Tang J, Ma J, Yi M, et al. Delay and diversity-induced synchronization transitions in a small-world neuronal network. Phys Rev E, 2011, 83: 046207

    Article  Google Scholar 

  48. Yilmaz E, Baysal V, Perc M, et al. Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network. Sci China Technol Sci, 2016, 59: 364–370

    Article  Google Scholar 

  49. Chen Y L, Yu L C, Chen Y. Reliability of weak signals detection in neurons with noise. Sci China Technol Sci, 2016, 59: 411–417

    Article  Google Scholar 

  50. Wang Z Q, Xu Y, Yang H. Lévy noise induced stochastic resonance in an FHN model. Sci China Technol Sci, 2016, 59: 371–375

    Google Scholar 

  51. Tang J, Jia Y, Yi M, et al. Multiplicative-noise-induced coherence resonance via two different mechanisms in bistable neural models. Phys Rev E, 2008, 77: 061905

    Article  Google Scholar 

  52. Tang J, Liu T B, Ma J, et al. Effect of calcium channel noise in astrocytes on neuronal transmission. Commun Nonlinear Sci Numer Simul, 2016, 32: 262–272

    Article  MathSciNet  Google Scholar 

  53. Jin W, Lin Q, Wang A, et al. Computer simulation of noise effects of the neighborhood of stimulus threshold for a mathematical model of homeostatic regulation of sleep-wake cycles. Complexity, 2017, 2017: 1–7

    Article  MathSciNet  MATH  Google Scholar 

  54. Li Q, Gao Y. Spiking regularity in a noisy small-world neuronal network. BioPhys Chem, 2007, 130: 41–47

    Article  Google Scholar 

  55. Zhou C, Kurths J, Hu B. Array-enhanced coherence resonance: Nontrivial effects of heterogeneity and spatial independence of noise. Phys Rev Lett, 2001, 87: 098101

    Article  Google Scholar 

  56. Sancho J M, San Miguel M, Katz S L, et al. Analytical and numerical studies of multiplicative noise. Phys Rev A, 1982, 26: 1589–1609

    Article  Google Scholar 

  57. Zhao Z, Gu H. Identifying time delay-induced multiple synchronous behaviours in inhibitory coupled bursting neurons with nonlinear dynamics of single neuron. Procedia IUTAM, 2017, 22: 160–167

    Article  Google Scholar 

  58. Gu H, Zhao Z. Dynamics of time delay-induced multiple synchronous behaviors in inhibitory coupled neurons. PLoS ONE, 2015, 10: e0138593

    Article  Google Scholar 

  59. Zhao Z, Gu H. The influence of single neuron dynamics and network topology on time delay-induced multiple synchronous behaviors in inhibitory coupled network. Chaos Solitons Fractals, 2015, 80: 96–108

    Article  MathSciNet  MATH  Google Scholar 

  60. Gu H, Pan B, Li Y. The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain. Nonlinear Dyn, 2015, 82: 1191–1210

    Article  MathSciNet  Google Scholar 

  61. Gu H G, Chen S G, Li Y Y. Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns. Chin Phys B, 2015, 24: 050505

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 2015XKMS080(JT)).

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Authors and Affiliations

  1. School of Physics, China University of Mining and Technology, Xuzhou, 221116, China

    Jun Tang & Juan Zhang

  2. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Jun Ma

  3. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China

    JinMing Luo

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  1. Jun Tang
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Correspondence to Jun Tang.

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Tang, J., Zhang, J., Ma, J. et al. Noise and delay sustained chimera state in small world neuronal network. Sci. China Technol. Sci. 62, 1134–1140 (2019). https://doi.org/10.1007/s11431-017-9282-x

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  • DOI: https://doi.org/10.1007/s11431-017-9282-x

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