Master of Science (MS)
First Committee Member
David G. Costa
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter ε:
u' = f (u) - ε h (t).
Namely, there exists an ε0 such that for 0 < ε < ε0 there are two periodic solutions, for ε = ε0 there is one periodic solution, and for ε >ε0 there are no periodic solutions, provided that....
In this paper we look at some numerical evidence regarding the behavior of this threshold for various types of harvesting terms, in particular we find evidence in the negative or a conjecture regarding the behavior of this threshold value.
Additionally, we look at analagous steady states for the reaction-diusion IBVP with logistic growth and positive harvesting: Using phase plane arguments we show that there is a threshold value of such that this BVP has no positive solutions.
Differential equations; Harvesting; Logistic; Periodic
Mathematics | Ordinary Differential Equations and Applied Dynamics
Palmer, Cody Alan, "Periodic Solutions and Positive Solutions of First and Second Order Logistic Type ODEs with Harvesting" (2012). UNLV Theses, Dissertations, Professional Papers, and Capstones. 1606.