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Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems
preprint
posted on 2006-02-13, 15:43 authored by S. CoombesWe discuss the notion of Liapunov exponent for integrate-and-fire (IF) type dynamical
systems. In contrast to smooth flows there is a contribution to the IF Liapunov
exponent arising from the discontinuous nature of the firing mechanism. Introducing
the notion of an IF mode-locked state we are able to show that linear stability
is consistent with the requirement of a negative IF Liapunov exponent. We apply
our results to IF systems that may be used to study the entrainment of biological
oscillators.
History
School
- Science
Department
- Mathematical Sciences
Pages
367899 bytesPublication date
1999Notes
This is a pre-print. The definitive version: COOMBES, S., 1999. Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems. Physics Letters A, 255(1-2), pp.49-57, is available at: http://www.sciencedirect.com/science/journal/03759601.Language
- en