Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 3 of 3
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
The Effect Of Habitat Fragmentation On Plant Communities In A Spatially-Implicit Grassland Model, Mika T. Cooney, Benjamin R. Hafner, Shelby E. Johnson, Sean Lee
The Effect Of Habitat Fragmentation On Plant Communities In A Spatially-Implicit Grassland Model, Mika T. Cooney, Benjamin R. Hafner, Shelby E. Johnson, Sean Lee
Rose-Hulman Undergraduate Mathematics Journal
The spatially implicit Tilman-Levins ODE model helps to explain why so many plant species can coexist in grassland communities. This now-classic modeling framework assumes a trade-off between colonization and competition traits and predicts that habitat destruction can lead to long transient declines called ``extinction debts.'' Despite its strengths, the Tilman-Levins model does not explicitly account for landscape scale or the spatial configuration of viable habitat, two factors that may be decisive for population viability. We propose modifications to the model that explicitly capture habitat geometry and the spatial pattern of seed dispersal. The modified model retains implicit space and is …
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Rose-Hulman Undergraduate Mathematics Journal
A system of first-order differential equations that arises in a model for the growth of microorganisms in a chemostat with Monod kinetics is studied. A new, semi-implicit numerical scheme is proposed to approximate solutions to the system. It is shown that the scheme is uniquely solvable and unconditionally stable, and further properties of the scheme are analyzed. The convergence rate of the numerical solution to the true solution of the system is given, and it is shown convergence of the numerical solutions to the true solutions is uniform over any interval [0, T ] for T > 0.
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae
Rose-Hulman Undergraduate Mathematics Journal
For the SCUDEM V 2020 virtual challenge, we received an outstanding distinction for modeling a bird perched on a bicycle wheel utilizing the appropriate physical equations of rotational motion. Our model includes both theoretical calculations and numerical results from applying the Heaviside function for the swing motion of the bird. We provide a discussion on: our model and its numerical results, the overall limitations and future work of the model we constructed, and the experience we had participating in SCUDEM V 2020.