Skip to main content
SpringerLink
Log in

Bifurcations Dynamics of Single Neurons and Small Networks

  • Living reference work entry
  • First Online:
Book cover Encyclopedia of Computational Neuroscience

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Belle M, Diekman C, Forger D, Piggins H (2009) Daily electrical silencing in the mammalian circadian clock. Science 326:281–284

    Article  PubMed  CAS  Google Scholar 

  • Bose A, Manor Y, Nadim F (2001) Bistable oscillations arising from synaptic depression. SIAM J Appl Math 62:706–727

    Article  Google Scholar 

  • Ermentrout GB (1996) Type i membranes, phase resetting curves and synchrony. Neur Comp 8:979–1001

    Article  CAS  Google Scholar 

  • Ermentrout GB, Kopell N (1998) Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc Natl Acad Sci 95:1259–1264

    Article  PubMed Central  PubMed  CAS  Google Scholar 

  • Ermentrout GB, Terman D (2010) Mathematical foundations of neuroscience. Springer, New York

    Book  Google Scholar 

  • Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer, New York

    Book  Google Scholar 

  • Izhikevich E (2000) Neural excitability, spiking and bursting. Int J Bifur Chaos 10:1171–1266

    Article  Google Scholar 

  • Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193–213

    Article  PubMed Central  PubMed  CAS  Google Scholar 

  • Nusse H, Ott E, Yorke J (1994) Border-collision bifurcations: an explanation for observed bifurcation phenomena. Phys Rev E 49:1073–1077

    Article  Google Scholar 

  • Rinzel J (1985) Bursting oscillations in an excitable membrane model. In: Sleeman B, Jarvis R (eds) Ordinary and partial differential equations: proceedings of the 8th Dundee conference, vol 1151, Lecture notes in mathematics. Springer, New York

    Chapter  Google Scholar 

  • Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Mathematical topics in population biology, morphogenesis and neurosciences, vol 71, Lecture notes in biomathematics. Springer, New York

    Google Scholar 

  • Rubin J, Shevtsova N, Ermentrout GB, Smith J, Rybak I (2009) Multiple rhythmic states in a model of the respiratory central pattern generator. J Neurophysiol 101:2146–2165

    Article  PubMed Central  PubMed  Google Scholar 

  • Skinner F, Kopell N, Marder E (1994) Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. J Comput Neurosci 1:69–87

    Article  PubMed  CAS  Google Scholar 

  • van Vreeswijk C, Abbott L, Ermentrout GB (1994) When inhibition, not excitation synchronizes neural firing. J Comp Neurosci 1:313–321

    Article  Google Scholar 

  • Zhang Y, Bose A, Nadim F (2009) The influence of the a-current on the dynamics of an oscillator-follower feed-forward inhibitory network. SIAM J Appl Dyn Syst 8:1564–1590

    Article  PubMed Central  PubMed  Google Scholar 

Download references

Acknowledgment

This work was supported in part by NSF DMS 1122291.

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Prof. Amitabha Bose

Authors
  1. Prof. Amitabha Bose
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amitabha Bose .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Bose, A. (2014). Bifurcations Dynamics of Single Neurons and Small Networks. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_453-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_453-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

Publish with us

Policies and ethics

Search

Navigation