Abstract:
: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.
journal_name
J Comput Neuroscijournal_title
Journal of computational neuroscienceauthors
Bizzarri F,Brambilla A,Gajani GSdoi
10.1007/s10827-013-0448-6subject
Has Abstractpub_date
2013-10-01 00:00:00pages
201-12issue
2eissn
0929-5313issn
1573-6873journal_volume
35pub_type
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