Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Differential equations (2)
- Analysis (1)
- Biology (1)
- Continuous-time Markov chains (1)
- Dengue fever (1)
-
- Dynamical System (1)
- Dynamical systems (1)
- Dynamics (1)
- Eigenvalue (1)
- Epidemiological model (1)
- Gene networks (1)
- Generalized derivatives (1)
- Glucose-insulin kinetics (1)
- Lie algebra (1)
- Lie group (1)
- MCR method (1)
- Markov (1)
- Model (1)
- Molecular dynamics (1)
- Nonlinear equation (1)
- Nonsmooth dynamical systems (1)
- ODE (1)
- Ordinary least squares (OLS) (1)
- Parameter estimation (1)
- Riot behavior (1)
- SIR model (1)
- SIS (1)
- Sensitivity analysis (1)
- Social contagions (1)
- Solution (1)
Articles 1 - 7 of 7
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Electronic Theses and Dissertations
Systems of ordinary differential equations (ODEs) may be used to model a wide variety of real-world phenomena in biology and engineering. Classical sensitivity theory is well-established and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the real-world system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical theory …
An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber
An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber
Electronic Theses and Dissertations
Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way …
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Electronic Theses and Dissertations
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …
Application Of Symplectic Integration On A Dynamical System, William Frazier
Application Of Symplectic Integration On A Dynamical System, William Frazier
Electronic Theses and Dissertations
Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic …
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Electronic Theses and Dissertations
Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …
Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker
Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker
Electronic Theses and Dissertations
Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …
A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach
A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach
Electronic Theses and Dissertations
In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model