First return maps for the dynamics of synaptically coupled conditional bursters

  title={First return maps for the dynamics of synaptically coupled conditional bursters},
  author={Evandro Manica and Georgi S. Medvedev and Jonathan E. Rubin},
  journal={Biological Cybernetics},
The pre-Bötzinger complex (preBötc) in the mammalian brainstem has an important role in generating respiratory rhythms. An influential differential equation model for the activity of individual neurons in the preBötc yields transitions from quiescence to bursting to tonic spiking as a parameter is varied. Further, past work has established that bursting dynamics can arise from a pair of tonic model cells coupled with synaptic excitation. In this paper, we analytically derive one- and two… CONTINUE READING


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 34 references

Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students

  • B Ermentrout
  • Software Environ. Tools 14,
  • 2002
Highly Influential
3 Excerpts

Bursting oscillations in an excitable membrane model. In: Sleeman BD, Jarvis RJ (eds) Ordinary and partial differential equations

  • J Rinzel
  • 1985
Highly Influential
5 Excerpts

Applications of chaos control techniques to a three-species food chain

  • AA Gomes, E Manica, MC Varriale
  • Chaos Solitons Fractals
  • 2008
1 Excerpt

Applications of the poincaré mapping technique to analysis of neuronal dynamics

  • P Jr.Channell, G Cymbalyuk, A Shilnikov
  • Neurocomputing
  • 2007

Similar Papers

Loading similar papers…