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Encyclopedia of Computational Neuroscience pp 39–41Cite as

Dynamical Systems: Overview

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Definition

Many models of computational neuroscience are formulated in terms of nonlinear dynamical system (sometimes the dynamical system with noise) and include a large number of parameters. Therefore, it is difficult to analyze dynamics and find correspondence between parameter values and dynamical mode. Mathematical theory of dynamical systems and bifurcations provide a valuable tool for a qualitative study and finding regions in parameter space corresponding to different dynamical modes (e.g., oscillations or bistability). Thus, the dynamical systems (or nonlinear dynamics) approach to analysis of neural systems has played a central role for computational neuroscience for many years (summarized, e.g., in recent textbooks, Izhikevich (2007) and Ermentrout and Terman (2010)).

Detailed Description

Theory of dynamical systems and bifurcations provides a list of universal scenarios of dynamics changes under parameter variation. For example, one scenario explaining the onset of...

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References

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

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  • Fitzhugh R (1955) Mathematical models of threshold phenomena in the nerve membrane. Bull Math Biophys 17(4):257–278

    Google Scholar 

  • Hodgkin AL (1948) The local electric changes associated with repetitive action in a non-medullated axon. J Physiol Lond 107:165–181

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  • Izhikevich EM (2007) Dynamical systems in neuroscience: the geometry of excitability and bursting. MIT Press, Cambridge, MA

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  • Rinzel J, Ermentrout B (1998) Analysis of neural excitability and oscillations. In: Koch C, Segev I (eds) Methods in neuronal modeling: from ions to networks, 2nd edn. MIT Press, Cambridge, MA, pp 251–291

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Utah, Salt Lake City, UT, 84112, USA

    Alla Borisyuk

Authors
  1. Alla Borisyuk
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Correspondence to Alla Borisyuk .

Editor information

Editors and Affiliations

  1. Department of Biology, Emory University, Atlanta, GA, USA

    Dieter Jaeger

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

    Ranu Jung

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Borisyuk, A. (2015). Dynamical Systems: Overview. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6675-8_768

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