Thèse doctorat : Génie Electrique. Composants et Systèmes Electriques : Villeurbanne, INSA : 2005. / Titre provenant de l'écran-titre. Bibliogr. p. 127-142.

Reproduction de : Habilitation à diriger des recherches : Sciences : Toulon : 2004. / Titre provenant du cadre-titre.

Reproduction de : Thèse doctorat : Génie informatique, automatique et traitement du signal : Reims : 2006. / Titre provenant de l'écran titre. Bibliogr. f. 131-137.

Reproduction de : Thèse de doctorat : Mathématiques : Lyon 1 : 2002. / Titre provenant de l'écran titre. 68 réf. bibliogr.

Not available / text

No description available.

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

Cheyne-Stokes respiration is a distinct breathing pattern consisting of periods of hyperpnea followed by apneas, with unknown etiology. One in two patients with congestive heart failure suffer 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. A mathematical model of the cardio-respiratory system was constructed using parameter values from real data. Hopf bifurcation analysis was used to determine regions of stable versus oscillatory breathing patterns. In the model, Cheyne-Stokes respiration is more likely to occur while in the supine position and males are more likely to develop Cheyne-Stokes than females. These findings, which are in agreement with clinical experience, suggest that both gender and fluid shift contribute to the pathogenesis of Cheyne-Stokes respiration, and that physical quantities such as blood volumes and neural feedback may be sufficient to explain the observations of CSR. / Department of Mathematics and Statistics

The bony fin rays of the zebrafish caudal fin are a convenient system for studying bone morphogenesis and patterning. Joints and bifurcations in fin rays follow predictable spatial patterns, though the mechanisms underlying these patterns are not well understood. We developed simulation models to explore ray pattern formation mechanisms in growing fins. In all models, the fin ray growth rates are based on quantitative experimental data. The different models simulate ray joint formation and bifurcation formation using different hypothetical mechanisms. In the most plausible model, ray joint and bifurcation formation result from the accumulation of two substances, arbitrarily named J and B. Model parameters were optimized to find the best fit between model output and quantitative experimental data on fin ray patterns. The model will be tested in the future by evaluating how well it can predict fin ray patterns in different fin shapes, mutant zebrafish fins, and other fish species.

In this thesis, bifurcation phenomena in dynamical systems with cosymmetry and Hamiltonian structure were investigated using numerical methods. Several numerical continuation methods and test functions for detecting bifurcations were presented. The numerical results for various examples are given using a numerical bifurcation analysis toolbox.