Lyapunov exponents computation for hybrid neurons

Lyapunov exponents are a basic and powerful tool to characterise the long-term behaviour of dynamical systems. The computation of Lyapunov exponents for continuous time dynamical systems is straightforward whenever they are ruled by vector fields that are sufficiently smooth to admit a variational m...

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Bibliographic Details
Published in:Journal of computational neuroscience Vol. 35; no. 2; pp. 201 - 212
Main Authors: Bizzarri, Federico, Brambilla, Angelo, Storti Gajani, Giancarlo
Format: Journal Article
Language:English
Published: Boston Springer US 01.10.2013
Springer Nature B.V
Subjects:
Algorithms
Biomedical and Life Sciences
Biomedicine
Brain - physiology
Computer Simulation
Electrophysiological Phenomena - physiology
Human Genetics
Models, Neurological
Nerve Net
Neural Networks (Computer)
Neurology
Neurons - physiology
Neurosciences
Theory of Computation
Variational model
Hybrid model
Neuron networks
Integrate and fire neuron
Lyapunov exponent
Saltation Matrix
ISSN:0929-5313, 1573-6873, 1573-6873
Online Access:Get full text
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Summary:Lyapunov exponents are a basic and powerful tool to characterise the long-term behaviour of dynamical systems. The computation of Lyapunov exponents for continuous time dynamical systems is straightforward whenever they are ruled by vector fields that are sufficiently smooth to admit a variational model. Hybrid neurons do not belong to this wide class of systems since they are intrinsically non-smooth owing to the impact and sometimes switching model used to describe the integrate-and-fire (I&F) mechanism. In this paper we show how a variational model can be defined also for this class of neurons by resorting to saltation matrices. This extension allows the computation of Lyapunov exponent spectrum of hybrid neurons and of networks made up of them through a standard numerical approach even in the case of neurons firing synchronously.
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ISSN:0929-5313
1573-6873
1573-6873
DOI:10.1007/s10827-013-0448-6