William F. Langford

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This paper initiates the classification, up to symmetry-covariant contact equivalence, of perturbations of local Hopf bifurcation problems which do not satisfy the classical non-degeneracy conditions. The only remaining hypothesis is that +i should be simple eigenvalues of the linearized right-hand side at criticality. Then the Lyapunov-Schmidt method(More)
"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)
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)
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)
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)
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)
This paper presents a study of the effects of symmetry on the generic bifurca-tion at a double-zero eigenvalue that was first investigated by Bogdanov and Takens. Two different symmetry groups are considered: Huygens symmetry and odd-Huygens symmetry. Here Huygens symmetry means that the system is equivariant under permutation of the two state variables.(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)
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