Henry C. Tuckwell: Articles in chronological order
2006
Cortical network modeling: Analytical methods for
firing rates
and some properties of networks of
LIF neurons
Journal of Physiology - Paris
100 (2006) 88–99
Spatial neuron model with two-parameter
Ornstein–Uhlenbeck input
current
2005
Time to first spike in stochastic
Hodgkin-Huxley systems
On the possible use of
Neurocomputing
67, 450-457, 2005.
Spike trains in a stochastic Hodgkin-Huxley
system.
Viral population growth models. 2nd Edition.
Encyclopedia of Biostatistics
2nd Edition, 2005 (Wiley,
2004
Firing properties of a stochastic PDE
model of a rat sensory cortex layer 2/3 pyramidal cell.
Mathematical Biosciences
188, 117-132, 2004.
Some optimal stochastic control
problems in Neuroscience.
Modern Physics Letters B 18, 1067-1085, 2004.
A note on vaccination against
meningococcal meningitis in infants.
Epidemiology
and Infection 132, 999-1000. (2004).
On the behavior of solutions in viral dynamical models.
2003
Determination
of firing times for the stochastic Fitzhugh-Nagumo model.
Neural Computation 15,
143-159, 2003.
Optimal control of neuronal activity.
Physical Review Letters 91,
018101, 2003.
Methods of Computational
Neuroscience: An Overview. (with J-F. Feng).
In,
Computational Neuroscience: A Comprehensive Approach, Feng,J-F. Ed.}
CRC,
A mathematical model for evaluating
the impact of vaccination schedules: application to Neisseria meningitidis.
Epidemiology and Infection, 130, 419-(2003).
2002
Analytical determination
of firing times in stochastic nonlinear neural models.
Neurocomputing 48, 1003-1007, 2002.
A spatial stochastic neuronal model with Ornstein-Uhlenbeck input current.
Biological Cybernetics 86, 137-145, 2002.
2001
On distributions of physiological and
anatomical variables in pathological conditions:
dopamine D2 receptors in schizophrenia
and their occupancies after drug treatment.
J Theoret Medicine 3, 213-220,
2001
Epidemic spread and bifurcation
effects in tw0-dimensional network models with viral dynamics.
Physical Review E 64, 041918, 2001
2000
A dynamical system for the approximate
moments of nonlinear stochastic models of spiking neurons and networks.
Mathematical and Computer
Modeling 31, 175-180, 2000
Cortical potential distributions and
information processing.
Neural Computation 12, 2777-2795, 2000
Enhancement of epidemic spread by
noise and stochastic resonance in spatial network models with viral dynamics.
Physical Review E 61, 5611-5619,
2000
Nature of equilibria and
effects of drug treatments in some viral
population dynamical models.
IMA J
Math.Appl.Biol.Med. 17, 311-327, 2000.
First passage time to detection in
stochastic population dynamical models for HIV-1
Applied Math Lett 13, 79-83, 2000
Interaction between viral population
dynamics and demography in the spread of disease.
1999
Repeating triplets of spikes and oscillations in the
mitral cell discharges of freely breathing rats.
European J. Neuroscience 11, 3185-3193, 1999
Direct HIV testing in blood donations: variation of
the yield with detection threshold and pool size.
Transfusion 39, 1141-1144, 1999.
A Bayesian method for combining
statistical tests.
J. Statistical Planning
& Inference 78, 317-323, 1999.
1998
Analytical and simulation results for
stochastic Fitzhugh-Nagumo neurons and neural networks.
J. Computational Neuroscience 5, 91-113, 1998.
Continuum models in neurobiology and
information processing.
The significance of precisely
replicating patterns in mammalian CNS spike trains.
Neuroscience 82, 315-336, 1998.
Variability in early HIV-1 population
dynamics.
A stochastic model for early HIV-1
population dynamics.
J Theor Biol 195, 451-463, 1998.
Spatial epidemic network models with viral dyamics.
Physical Review E 57,2163-2169, 1998.
1997
Population growth with randomly
distributed jumps.
J.
Mathematical Biology 36, 169-187, 1997.
Coding of odour intensity in a sensory
neuron.
Reliability of spike encoding in
cortical neurons.
On the simulation of biological
diffusion processes.
Comput. Biol. Med. 27,
1-7, 1997.
1996
Statistical properties of stochastic
nonlinear dynamical models of single spiking neurons and neural networks.
Physical Review E 54, 5585-5590, 1996
On the concentration of 5-HIAA in
schizophrenia: a meta-analysis.
Psychiatry Research 59, 239-244, 1996.
Time-dependent solutions for a cable
model of an olfactory receptor neuron.
J. Theor. Biol. 181, 25-31, 1996.
Coding of stimulus intensity in an
olfactory receptor neuron.
Bulletin Math Biol 58, 493-512, 1996.
Coding of odor intensity in a
deterministic model of an olfactory receptor neuron.
J. Computational Neuroscience 3, 51-72, 1996.
1995
Some new results on the coding of
pheromone intensity in an olfactory sensory
neuron.
1994
A weighted nonparametric procedure for
the combination of events.
Biometrical J. 36,
1005-1012, 1994.
Synaptic modeling: Cofactor modifications to
Michaelis-Menten kinetics.
1993
World and regional populations.
A meta-analysis of homovanillic acid
concentrations in schizophrenia.
International J Neuroscience 73, 109-114, 1993.
Dynamical models of central nervous system synapses:
the role of chemical kinetic theory.
Voltage clamp
calculations for myelinated and demyelinated axons.
European
Biophysical J. 22, 71-77, 1993.
1992
Random
perturbations of the reduced Fitzhugh-Nagumo equation.
Physica Scripta 46, 481-484, 1992
World population.
Simple mathematical models for urban
growth.
Proc. Roy. Soc. A 438,
171-181, 1992.
On the effects of random perturbations in a nonlinear
system.
J. Chem Phys 97, 7013-7014, 1992
Shift of equilibria by noise.
Aust National Univ Report 1992
1989
A neurophysiological theory of a
reproductive process.
International J Neuroscience 44, 143-148, 1989.
1988
Nonlinear random reaction-diffusion
systems.
Biomathematics and related computational problems,
1988
Perturbative analysis of random
nonlinear reaction-diffusion systems.
Physica Scripta 37, 321-322, 1988.
Use of Green's function matrices for
systems of diffusion equations.
International J. Systems Science 1988
1987
Statistical properties of perturbative
nonlinear random diffusion from stochastic integral representations.
Physics Letters A 122, 117-120,
1987.
Techniques for obtaining analytical
solutions for Rall's model neuron.
J.
Neuroscience Methods 20, 151-166, 1987.
Diffusion approximations to
channel noise.
J. Theor. Biol.127, 427-438, 1987.
Logistic population growth under
random dispersal.
Bulletin Math Biol 49,
495-506, 1987.
1986
On shunting inhibition.
Biological Cybernetics 55, 83-90, 1986
Stochastic equations for nerve
membrane potential.
J. Theoretical Neurobiology 5, 87-99, 1986.
Population projections for
New Zealand Stat 21, 35-40, 1986.
1985
Some aspects of cable theory with
synaptic reversal potentials.
J. Theoretical Neurobiology
4, 113-127, 1985.
Determination of the electrical
potential over dendritic trees by mapping onto a nerve cylinder.
J. Theoretical
Neurobiology 4, 27-46, 1985.
1984
Neuronal response to stochastic stimulation.
IEEE Syst Man Cyb 14, 464-469, 1984.
The interspike interval of a cable
model neuron with white noise input.
Biological Cybernetics 49,
155-167, 1984.
First passage time of Markov processes
to moving barriers.
J. Applied Probability 21, 695-709, 1984.
1983
Random currents through nerve
membranes.
Biological Cybernetics 49,
99-110, 1983.
1982
Effect of field geometry on the spread
of crop disease.
Protection Ecology 4, 81-108, 1982.
Matrix methods for predicting
Neuronal firing and input variability.
J. Theoretical
Neurobiology 1, 197-218, 1982.
1981
Simplifed reaction-diffusion
equations for potassium and calcium ion concentrations during spreading
cortical depression.
International J.
Neuroscience 12, 95-107, 1981.
Poisson processes in biology.
Stochastic Nonlinear Systems 1981.
Ion and transmitter movements during
spreading cortical depression.
International
J. Neuroscience 12, 109-135, 1981.
Logistic growth with random density
independent disasters.
Theoretical Population
Biology 19, 1-18, 1981.
1980
Accuracy of neuronal interspike times
calculated from a diffusion approximation.
J. Theor. Biol. 83,
377-387, 1980.
The response of a nerve cylinder to
spatially distributed white noise inputs.
J. Theor. Biol.87, 275-295, 1980.
Evidence of soliton-like behavior of
solitary waves in a nonlinear reaction-diffusion system.
SIAM J Applied Math 39, 310-322, 1980.
Predictions and properties of a model
of potassium and calcium ion movements during spreading cortical
depression
International J. Neuroscience 10, 145-164,
1980.
1979
Synaptic transmission in a model for stochastic
neuronal activity.
J. Theor. Biol. 77, 65-81, 1979.
Firing rates of neurons with random
excitation and inhibition.
J. Theor. Biol.80, 1-14, 1979.
The response of a spatially
distributed neuron to white noise current injection.
Biological Cybernetics 33, 39-55, 1979.
Solitons in a reaction-diffusion
system.
1978
Analysis and estimation of synaptic
densities and their spatial variation on the motoneuron surface.
Brain Research 150, 617-624,
1978.
A mathematical model for spreading
cortical depression.
Biophysical J. 23, 257-276, 1978.
Repetitive subthreshold synaptic
excitation and transmitter depletion.
J. Theor. Biol.70, 467-469,
1978.
Recurrent inhibition and
afterhyperpolarization: effects on neuronal discharge.
Biological Cybernetics 30, 115-123,
1978
Neuronal interspike time histograms
for a random input model.
Biophysical J.21, 289-290, 1978.
Neuronal interspike time distributions and the estimation of neurophysiological and neuroanatomical parameters.
J. Theor. Biol. 71, 167-183, 1978.
A review of Models of the Stochastic
Activity of Neurons by A.V. Holden.
Is there a connection between coma
and spreading cortical depression?
Persistence times of populations
with large random fluctuations.
Theoretical Population
Biology 14, 46-61, 1978.
Eradication
times of cell populations with random killing of fractions of the cell mass.
1977
On stochastic models of the activity
of single neurons.
J. Theor. Biol. 65, 783-785, 1977.
1976
Firing rates of motoneurons with
strong random synaptic excitation.
Biological Cybernetics 24, 147-152, 1976.
Frequency of firing of Stein's model
neuron with application to cells of the dorsal spinocerebellar tract.
Brain Research 116, 323-328, 1976.
The effects of random selection on
gene frequency.
Mathematical Biosciences 30, 113-128, 1976.
Stochastic integrals and their
relation to some diffusion models of population growth and gene frequency.
On the first exit time problem for
temporally homogeneous Markov processes.
J. Applied Probability 13, 39-48, 1976.
Effects of partial cross sections on
the energy distribution of slow secondary electrons.
J. Chem Phys 64, 333-336, 1976.
1975
Determination of the inter-spike times
of neurons receiving randomly arriving postsynaptic potentials.
Biological Cybernetics 18, 225-237,1975.
1974
Some stochastic growth processes
Mathematical Problems in Biology 1974
Viability effects on
density-independent population growth.
A diffusion model for Gompertzian
growth.
A study of some diffusion models of
population growth.
Theor. Pop. Biol. 5, 345-357,
1974,
1973
Transition densities for some classes
of biological random processes.
1971
On the photoionization cross section and Rydberg
series of O2.
J Quant Spect Rad Transf 11, 391-397, 1971.
1970
On the validity of the Franck-Condon
factor approximation for photo-ionizing transitions of O2.
J Quant Spect Rad Transf 10, 653-657, 1970.
Calculation of the photoionization cross section of
N2 from first threshold to 500 Angstroms