William F. Langford

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"Mayer waves" are long-period (6 to 12 seconds) oscillations in arterial blood pressure, which have been observed and studied for more than 100 years in the cardiovascular system of humans and other mammals. A mathematical model of the human cardiovascular system is presented, incorporating parameters relevant to the onset of Mayer waves. The model is(More)
This paper investigates generic bifurcations from a D m-invariant equilibrium of a D m-symmetric dynamical system, for m = 3 or 4, near points of codimension-2 steady-state mode interactions. The center manifold is isomorphic to IR 3 or IR 4 and is non-irreducible. Depending on the group representation, in the unfolding of the linearization we nd:(More)
Double Hopf bifurcations have been studied prior to this work in the generic nonresonant case and in certain strongly resonant cases, including 1:1 resonance. In this paper, the case of symmetrically coupled identical oscillators, motivated by the classic problem of synchronization of Huygens’ clocks, is studied using the codimension-three Elphick–Huygens(More)
Cheyne-Stokes respiration (CSR) is a periodic breathing pattern, characterized by short intervals of very little or no breathing (apnea), each followed by an interval of very heavy breathing (hyperpnea). This work presents a new compartmental model of the human cardio-respiratory system, simulating the factors that determine the concentrations of carbon(More)
Cheyne-Stokes respiration is a distinct breathing pattern consisting of periods of hyperpnea followed by apnoeas, with unknown aetiology. One in two patients with congestive heart failure suffers from this condition. Researchers hypothesize that key factors in CSR are the fluid shift from the standing to supine position and the differences between genders.(More)
In 1665, Huygens observed that two identical pendulum clocks, weakly coupled through a heavy beam, soon synchronized with the same period and amplitude but with the two pendula swinging in opposite directions. This behaviour is now called anti-phase synchronization. This paper presents an analysis of the behaviour of a large class of coupled identical(More)
A mathematical model of convection of a Boussinesq fluid in a rotating spherical shell is analyzed using numerical computations guided by bifurcation theory. The fluid is differentially heated on its inner spherical surface, with the temperature increasing from both poles to a maximum at the equator. The model is assumed to be both rotationally symmetric(More)
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