Definition
In neural population models (NPMs), as in dynamical systems in general, smooth changes in system parameters, for example, coupling strength, input levels, and time constants, may result in sudden qualitative changes in system dynamics, such as the occurrence or disappearance of oscillatory or chaotic behavior. Such phenomena are referred to as bifurcations and are interesting because they may account for switching phenomena, which are common in both brain signals and organisms’ behavior.
Detailed Description
Depending on their particular parameter set, NPMs experience different asymptotic dynamic behaviors characterized by constant output, harmonic (i.e., sinusoidal) or nonharmonic oscillations, which can be periodic or quasiperiodic (i.e., the signal repeats itself approximately, but not exactly), and even chaotic behavior (Frascoli et al. 2011; Spiegler et al. 2010, 2011). The transitions in parameter space between these qualitatively different states are called...
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References
Breakspear M, Jirsa VK (2007) Neuronal dynamics and brain connectivity. In: Jirsa VK, McIntosh AR (eds) Handbook of brain connectivity, 1st edn. Springer, Berlin/Heidelberg/New York, pp 3–64
Frascoli F, van Veen L, Bojak I, Liley DTJ (2011) Metabifurcation analysis of a mean field model of the cortex. Physica D 240(11):949–962
Grimbert F, Faugeras O (2006) Bifurcation analysis of Jansen’s neural mass model. Neural Comput 18:3052–3068
Guckenheimer J (2007) Bifurcations. Scholarpedia 2(6):1517. http://www.scholarpedia.org/article/Bifurcations. Accessed 21 Mar 2013
Jansen BH, Rit VG (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled columns. Biol Cybern 73:357–366
Kuznetsov Y (2004) Elements of applied bifurcation theory, 3rd edn. Springer, New York
Spiegler A, Kiebel SJ, Atay FM, Knösche TR (2010) Bifurcation analysis of neural mass models: impact of extrinsic inputs and dendritic time constants. Neuroimage 52:1041–1058
Spiegler A, Knösche TR, Schwab K, Haueisen J, Atay FM (2011) Modeling brain resonance phenomena using a neural mass model. PLoS Comput Biol 7:e1002298
Touboul J, Faugeras O (2007) Codimension two bifurcations and rhythms in neural mass models. arXiv:0907.2718 [math.DS]
Touboul J, Wendling F, Chauvel P, Faugeras O (2011) Neural mass activity, bifurcations, and epilepsy. Neural Comput 23:3232–3286
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Knösche, T.R. (2014). Bifurcations, Neural Population Models and. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_53-2
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_53-2
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Bifurcations, Neural Population Models and- Published:
- 30 July 2014
DOI: https://doi.org/10.1007/978-1-4614-7320-6_53-2
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Bifurcations, Neural Population Models and- Published:
- 07 February 2014
DOI: https://doi.org/10.1007/978-1-4614-7320-6_53-1