Global ETD Search
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Showing 1 to 8 of 8 for “"Geometric singular perturbation theory"”.
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Analysis and implementation of robust numerical methods to solve mathematical models of HIV and Malaria co-infection
… into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical …
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A Dynamical Study of the Poisson-Nernst-Planck System for Three Ions
… charge zero. The PNP system can be treated as singularly perturbed system that has two limiting systems: inner and outer systems (termed fast and slow system in geometric singular perturbation theory). A complete set of integrals for the inner system is presented that provides information for …
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A Mathematical Model for the Transition in Firing Patterns Across Puberty of a Gonadotropin-Releasing Hormone Neuron
… of the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems that comprise the core results of my thesis.</p>
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Two-patch herbivore/vegetation models with density-dependent migration
… demographic changes in the system. We used the geometric singular perturbation theory in order to reduce the dimension of the system. Using the continuation software AUTO we provided bifurcation diagrams for the reduced systems and we also provided some numerical illustrations to show the …
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The control of frequency of a conditional oscillator simultaneously subjected to multiple oscillatory inputs
… set of equations are obtained analytically using geometric singular perturbation theory and an analytic approximation of the frequency is obtained. The results are validated through numerical simulations of the model and are shown to extend to a detailed Hodgkin-Huxley type compartmental model of …
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Rate-induced tipping to metastable Zombie fires
… compactification technique with concepts from geometric singular perturbation theory. This framework allows us to reduce a reversible R-tipping problem due to crossing a quasithreshold to a heteroclinic orbit problem in a singular limit. Thus, we identify generic cases of such R-tipping via: …
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The role of short term synamptic plasticity in temporal coding of neuronal networks
… the spiking neurons and we use techniques from geometric singular perturbation theory to show that any n-cluster solution must satisfy a set of consistency conditions that can be geometrically derived. The results of both problems are validated using numerical simulations.
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Analysis and reduction of a modeled bursting neuron
… neuron was analyzed using methods based upon geometric singular perturbation theory. The mathematical mechanism of bursting in the model consisted of two slow variables traversing the state-space across a saddle-node bifurcation that defined an interface between quiescence and periodic spiking …