Khajeh Alijani, Azadeh (2011) Deterministic and stochastic dynamics of multi-variable neuron models : resonance, filtered fluctuations and sodium-current inactivation. PhD thesis, University of Warwick.

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Abstract

Neurons are the basic elements of the networks that constitute the computational
units of the brain. They dynamically transform input information into
sequences of electrical pulses. To conceive the complex function of the brain,
it is crucial to understand this transformation and identify simple neuron models
which accurately reproduce the known features of biological neurons. This thesis
addresses three different features of neurons.
We start by exploring the effect of subthreshold resonance on the response
of a periodically forced neuron using a simple threshold model. The response is
studied in terms of an implicit one-dimensional time map that corresponds to the
Poincar´e map of the forced system. Qualitatively distinct responses are found,
including mode locking and chaos. We analytically find the stability regions of
mode-locking solutions, and identify the transition to chaos through period-adding
bifurcations. We show that the response becomes chaotic when the forcing frequency
is close to the resonant frequency.
Then we will consider an experimentally verified model with realistic spikegenerating
mechanism and study the effect of filtered synaptic fluctuations on the
firing-rate response of the neuron. Using a population density method as well as an
efficient numerical method, we find the steady-state firing rate in two limits of fast
and slow synaptic inputs and present the linear response theory for the firing rate
of the model in response to both time-dependent mean inputs and time-dependent
noise intensity.
Finally, a novel model is introduced that incorporates threshold variability
of neurons. We determine the modulation of the input-output properties of the
model due to oscillatory inputs and in the presence of filtered synaptic fluctuations.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QP Physiology
Library of Congress Subject Headings (LCSH):	Neurons -- Mathematical models
Official Date:	January 2011
Dates:	Date Event January 2011 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Baesens, Claude ; Richardson, Magnus
Sponsors:	University of Warwick ; Overseas Research Students Awards Scheme (ORSAS)
Extent:	xxv, 178 leaves : ill., charts
Language:	eng

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