Henry C. Tuckwell

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A mathematical model is derived from physiological considerations for slow potential waves (called spreading depression) in cortical neuronal structures. The variables taken into account are the intra- and extracellular concentrations of Na+, Cl-, K+, and Ca++, together with excitatory and inhibitor transmitter substances. The general model includes(More)
A stochastic model equation for nerve membrane depolarization is derived which incorporates properties of synaptic transmission with a Rall-Eccles circuit for a trigger zone. If input processes are Poisson the depolarization is a Markov process for which equations for the moments of the interspike interval can be written down. An analytic result for the(More)
The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions(More)
Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major(More)
Electrophysiological properties of spiking neurons receiving complex stimuli perturbed by noise are investigated. A semi-analytical estimate of firing probabilities and subthreshold behavior of the stochastic system can be made in terms of the solution of a purely deterministic system. The method comes from an approximation for the distribution function and(More)
We investigate the properties of a simple discrete time stochastic epidemic model. The model is Markovian of the SIR type in which the total population is constant and individuals meet a random number of other individuals at each time step. Individuals remain infectious for R time units, after which they become removed or immune. Individual transition(More)
We investigated the effects of noise on periodic firing in the Hodgkin-Huxley nonlinear system. With mean input current mu as a bifurcation parameter, a bifurcation to repetitive spiking occurs at a critical value microc approximately 6.44 . The firing behavior was studied as a function of the mean and variance of the input current, firstly with initial(More)
We examine some simple mathematical models which have been recently employed to predict the evolution of population dynamical systems involving virus particles. They include: (1) A general two-component antibody-viral system; (2) A simplified two-component model for HIV-1 dynamics (3) An HIV-1 three-component model including virions and (4) A four-component(More)
The first three moments of the interspike interval are determined for Poisson excitation of a neuron with exponentially decaying membrane potential and a fixed threshold for action potentials. Analytic calculations are presented for the first and second moments for small threshold to EPSP ratios and a wide range of input frequencies. The coefficient of(More)
The inhibitory influences of recurrent inhibition and afterhyperpolarization are studied theoretically insofar as they affect the density of the interspike interval and the frequency transfer characteristic. The methods employed involve exact results for excitation with decay and constant threshold, computer simulations for decaying thresholds representing(More)