Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Dynamic Systems (2)
- Ordinary Differential Equations and Applied Dynamics (2)
- Astrophysics and Astronomy (1)
- Biology (1)
- Computer Sciences (1)
-
- Dynamical Systems (1)
- Geometry and Topology (1)
- Life Sciences (1)
- Mathematics (1)
- Non-linear Dynamics (1)
- Numerical Analysis and Computation (1)
- Numerical Analysis and Scientific Computing (1)
- Other Mathematics (1)
- Partial Differential Equations (1)
- Physical Processes (1)
- Programming Languages and Compilers (1)
- Stars, Interstellar Medium and the Galaxy (1)
- Theory and Algorithms (1)
- Institution
- Publication
- Publication Type
Articles 1 - 4 of 4
Full-Text Articles in Other Applied Mathematics
The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel
The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel
CURE Proceedings
The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Williams Honors College, Honors Research Projects
In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating …
Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria
Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria
Applications and Applied Mathematics: An International Journal (AAM)
The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …
A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark
A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark
Theses and Dissertations
This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.