Abstract
Mathematical modeling has been and will continue to be central to the understanding of the emerging function of the nervous system. From the firing of action potentials – with their all-or-none characteristic – to the rich dynamical repertoire of neural networks, the equations and numerical models that describe them are a key part of our understanding of the nervous system. Moreover, they continue to be the subject of further research. In this chapter, we will describe what a mathematical model is and why it is useful. Then, we will describe models of neurons and networks of neurons, emphasizing on how the biophysical concepts are translated to equations.
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Notes
- 1.
Hidden Markov model is a statistical model in which the system being modeled is assumed to be a Markov process with unobserved (i.e., hidden) states. A Markov process is one in which randomly changing systems are modeled assuming that future states depend only on the current state.
References
Izhikevich EM (2007) Dynamical systems in neuroscience. MIT press
Literature for Further Study
Brette R (2015) What is the most realistic single-compartment model of spike initiation? PLoS Comput Biol 11(4):e1004114. https://doi.org/10.1371/journal.pcbi.1004114
Gerstner W et al (2014) Neuronal dynamics: From single neurons to networks and models of cognition. Cambridge University Press
Miller P (2018) An introductory course in computational neuroscience. The MIT Press
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Orio, P. (2021). Mathematical Modeling in Neuroscience. In: Zeise, M.L. (eds) Neuroscience for Psychologists. Springer, Cham. https://doi.org/10.1007/978-3-030-47645-8_8
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DOI: https://doi.org/10.1007/978-3-030-47645-8_8
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