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Ordinary Differential Equations and Applied Dynamics Commons™
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- Non-linear conjugate gradient (2)
- Parameter estimation (2)
- Brain metabolism (1)
- Colon cancer (1)
- Cucurbita pollination (1)
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- Ecological Tipping Point (1)
- Esophageal cancer (1)
- Esophageal cancer. (1)
- Evolutionary game theory (1)
- Evolutionary resistance (1)
- Fokker–Planck optimization (1)
- Glucose metabolism model (1)
- HIV (1)
- Integrable evolution equations (1)
- Linear algebra (1)
- Mathematical Biology (1)
- Metabolic parametrization (1)
- Nash equilibrium (1)
- Obligate Mutualism (1)
- Optimal control (1)
- Peponapis pruinosa (1)
- Phenological Mismatch (1)
- Phenological Overlap (1)
- Plant-Pollinator Mutualism (1)
- Pollinator Decline (1)
- Pontryagin's minimum principle (1)
- Relaxation scheme (1)
- Squash Bee (1)
- Stackelberg equilibrium (1)
- Publication Type
Articles 1 - 5 of 5
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Phenological Overlap In Obligate Plant-Pollinator Mutualism, Austin J. Carlson
Phenological Overlap In Obligate Plant-Pollinator Mutualism, Austin J. Carlson
2026 Spring Honors Capstones Projects
Plant-pollinator mutualisms require temporal overlap between flowering and pollinator activity, so climate-driven timing shifts can weaken the interaction and, in severe cases, destabilize the system. This work investigates how reduced overlap affects persistence in an obligate plant-pollinator pair using a coupled differential equation model in which a phenological overlap factor scales the saturating mutualistic benefit. Simplification with a constant overlap enables closed-form equilibrium and stability analysis, revealing that below a critical overlap threshold, coexistence is no longer maintained. Rescaling reduces the parameter space from ten quantities to seven dimensionless groups, and sensitivity analysis identifies the degree of species dependence and …
Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi
Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi
Mathematics Dissertations - Archive
In this thesis, we employ optimal control frameworks in two distinct contexts: Human immunodeficiency virus (HIV) and esophageal cancer. For HIV, we introduce a comprehensive data-driven nonlinear optimization framework designed for personalized therapies. This framework utilizes a deterministic in-host nonlinear ordinary differential equation (ODE) model and formulates two optimization problems using individual patient data. The first problem focuses on estimating patient-specific parameters through constrained optimization, while the second problem determines optimal combination therapies to reduce viral load to undetectable levels. Several numerical experiments suggest that our framework can provide a robust and effective optimal dosages with lower toxicity levels to …
Integrable Evolution Equations, Ramesh C. Sharma
Integrable Evolution Equations, Ramesh C. Sharma
Mathematics Dissertations - Archive
Integrable evolution equations are certain nonlinear partial differential equations or semidiscrete nonlinear difference equations that are used to model wave propagation in various media. The goal of this thesis is to present the derivation of integrable evolution equations in a way accessible to nonexperts in the field of integrable systems and to illustrate those derivations by various explicit examples. In the case of nonlinear partial differential equations, both the spacial variable x and temporal variable t are continuous independent variables. In the case of semidiscrete nonlinear difference equations, the spacial variable n is a discrete independent variable and the temporal …
A New Mechanistic Model Of Brain Metabolism With Optimal Parametrization, Alice Lubbe
A New Mechanistic Model Of Brain Metabolism With Optimal Parametrization, Alice Lubbe
Mathematics Dissertations - Archive
Models of glucose metabolism in the brain often focus on chemical exchanges and reactions that occur as part of the tricarboxylic acid cycle (TCA cycle). Experiments involving nuclear magnetic resonance (NMR) spectroscopy to detect and measure carbon-labeled isotopomers of metabolites such as glutamate in vivo inform kinetic, mechanistic models used to study metabolic pathways. In the present work, a new model with two compartments, astrocytic and neuronal, is developed using known biochemical processes and fit to experimental data coming from fully labeled glucose infusions. A gradient descent method is introduced and employed to obtain optimal flux parameter values involved in …
A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd
A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd
Mathematics Dissertations - Archive
In this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the …