Journal article
First return maps for the dynamics of synaptically coupled conditional bursters
Biological cybernetics, v 103(2), pp 87-104
Aug 2010
PMID: 20614222
Abstract
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-dimensional maps from the differential equations for a self-coupled neuron and a two-neuron network, respectively. Using a combination of analysis and simulations of these maps, we explore the possible forms of dynamics that the model networks can produce as well as which transitions between dynamic regimes are mathematically possible.
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Details
- Title
- First return maps for the dynamics of synaptically coupled conditional bursters
- Creators
- Evandro Manica - Departamento de Matematica, Universidade Federal do Rio Grande do Sul, Porte Alegre, RS, CEP 91509-900, Brazil. evandro.manica@ufrgs.brGeorgi S MedvedevJonathan E Rubin
- Publication Details
- Biological cybernetics, v 103(2), pp 87-104
- Publisher
- Springer Nature; Germany
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000280065200001
- Scopus ID
- 2-s2.0-77955555364
- Other Identifier
- 991014878243204721
InCites Highlights
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Computer Science, Cybernetics
- Neurosciences