Abstract
Models of neurons based on iterative maps allows the simulation of big networks of coupled neurons without loss of biophysical properties such as spiking, bursting or tonic bursting and with an affordable computational effort. A piecewise linear two dimensional map with one fast and one slow variable is used to model spiking–bursting neural behavior. This map shows oscillations similar to other phenomenological models based on maps that require a much higher computational effort. The dynamics of coupled neurons is studied for different coupling strengths.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Izhikevich, E.M.: Neural Excitability, Spiking and Bursting. International Journal of Bifurcation and Chaos 10, 1171–1266 (2000)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and application to conduction and excitation in nerve. Journal of Physiology 117, 165–181 (1954)
Rose, R.M., Hindmarsh, J.L.: The assembly of ionic currents in a thalamic neuron, I The three dimensional model. Proceedings of The Royal Society of London B 237, 267–288 (1989)
Rulkov, N.F.: Modeling of spiking-bursting neural behavior using two–dimensional map. Physical Review E 65, 041922 (2002)
Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. on Neural Networks 68, 052901 (2003)
Elson, R.C., et al.: Synchronous Behavior of Two Coupled biological Neurons. Physical Review Letters 81(25), 5692 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aguirre, C., Campos, D., Pascual, P., Serrano, E. (2005). A Model of Spiking-Bursting Neuronal Behavior Using a Piecewise Linear Two-Dimensional Map. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_17
Download citation
DOI: https://doi.org/10.1007/11494669_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26208-4
Online ISBN: 978-3-540-32106-4
eBook Packages: Computer ScienceComputer Science (R0)