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Ordinary Differential Equations and Applied Dynamics Commons™
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- Basins of Attraction (1)
- Brachistochrone (1)
- Calcium dynamics (1)
- Cardiac muscle cell (1)
- Clocks (1)
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- Differential equation (1)
- Dynamical (1)
- Ecological (1)
- Force–calcium relationship (1)
- Hermitian (1)
- Homarus americanus (American lobster) (1)
- Managment (1)
- Mathematical model (1)
- Mathematics (1)
- Minimization (1)
- Nelder-Mead (1)
- Non-autonomous (1)
- Optimization (1)
- Physics (1)
- Quantum Mechanics (1)
- Radial (1)
- Sensitivity Analysis (1)
- Simplex (1)
- Stablilty (1)
- Tangential (1)
- Time (1)
Articles 1 - 5 of 5
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah
Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah
Honors Projects
The Nelder-Mead optimization method is a numerical method used to find the minimum of an objective function in a multidimensional space. In this paper, we use this method to study functions - specifically functions with three-dimensional graphs - and create images of the basin of attraction of the function. Three different methods are used to create these images named the systematic point method, randomized centroid method, and systemized centroid method. This paper applies these methods to different functions. The first function has two minima with an equivalent function value. The second function has one global minimum and one local minimum. …
Classifying Flow-Kick Equilibria: Reactivity And Transient Behavior In The Variational Equation, Alanna Haslam
Classifying Flow-Kick Equilibria: Reactivity And Transient Behavior In The Variational Equation, Alanna Haslam
Honors Projects
In light of concerns about climate change, there is interest in how sustainable management can maintain the resilience of ecosystems. We use flow-kick dynamical systems to model ecosystems subject to a constant kick occurring every τ time units. We classify the stability of flow-kick equilibria to determine which management strategies result in desirable long-term characteristics. To classify the stability of a flow-kick equilibrium, we classify the linearization of the time-τ map given by the time-τ map of the variational equation about the equilibrium trajectory. Since the variational equation is a non-autonomous linear differential equation, we conjecture that the asymptotic stability …
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
Honors Projects
In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …
Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, Stephen Ligtenberg
Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, Stephen Ligtenberg
Honors Projects
No abstract provided.
Mathematical Modeling Of The American Lobster Cardiac Muscle Cell: An Investigation Of Calcium Ion Permeability And Force Of Contractions, Lauren A. Skerritt
Mathematical Modeling Of The American Lobster Cardiac Muscle Cell: An Investigation Of Calcium Ion Permeability And Force Of Contractions, Lauren A. Skerritt
Honors Projects
In the American lobster (Homarus americanus), neurogenic stimulation of the heart drives fluxes of calcium (Ca2+) into the cytoplasm of a muscle cell resulting in heart muscle contraction. The heartbeat is completed by the active transport of calcium out of the cytoplasm into extracellular and intracellular spaces. An increase in the frequency of calcium release is expected to increase amplitude and duration of muscle contraction. This makes sense because an increase in cytoplasmic calcium should increase the activation of the muscle contractile elements (actin and myosin). Since calcium cycling is a reaction-diffusion process, the extent to …