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Nonlinear Dynamics

, Volume 78, Issue 1, pp 391–407 | Cite as

Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models

  • Huaguang GuEmail author
  • Baobao Pan
  • Guanrong Chen
  • Lixia Duan
Original Paper

Abstract

A series of bifurcations from period-1 bursting to period-1 spiking in a complex (or simple) process were observed with increasing extra-cellular potassium concentration during biological experiments on different neural pacemakers. This complex process is composed of three parts: period-adding sequences of burstings, chaotic bursting to chaotic spiking, and an inverse period-doubling bifurcation of spiking patterns. Six cases of bifurcations with complex processes distinguished by period-adding sequences with stochastic or chaotic burstings that can reach different bursting patterns, and three cases of bifurcations with simple processes, without the transition from chaotic bursting to chaotic spiking, were identified. It reveals the structures closely matching those simulated in a two-dimensional parameter space of the Hindmarsh–Rose model, by increasing one parameter \(I\) and fixing another parameter \(r\) at different values. The experimental bifurcations also resembled those simulated in a physiologically based model, the Chay model. The experimental observations not only reveal the nonlinear dynamics of the firing patterns of neural pacemakers but also provide experimental evidence of the existence of bifurcations from bursting to spiking simulated in the theoretical models.

Keywords

Bifurcation Neural firing Chaos Bursting  Spiking Period-adding bifurcation 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11372224 and 11072135, the Fundamental Research Funds for Central Universities designated to Tongji University under Grant No. 1330219127, and Hong Kong Research Grants Council under the GRF Grant CityU1109/12E.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Huaguang Gu
    • 1
    Email author
  • Baobao Pan
    • 1
  • Guanrong Chen
    • 2
  • Lixia Duan
    • 3
  1. 1.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina
  2. 2.Department of Electronic EngineeringCity University of Hong KongHong KongChina
  3. 3.College of ScienceNorth China University of TechnologyBeijingChina

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