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Full-Text Articles in Mathematics
Dynamics And Asymptotic Behavior Of The Solutions Of A Nonlinear Differential Equation, Robert Palmer
Dynamics And Asymptotic Behavior Of The Solutions Of A Nonlinear Differential Equation, Robert Palmer
Masters Theses & Specialist Projects
Initial value problems of the form dx/dt= t xP, x(a) = β are examined, first when p = 2. Applying Euler's method, a numerical approximation technique, when p = 2 for certain initial conditions produces a numerical solution which resembles a bifurcation diagram very similar to that produced by the logistic map. Comparisons of such numerical solutions to the logistic map are made, and a partial explanation of such numerical solutions is given. Then, the exact solution of the initial value problem with p = 2, for which the software package Mathematica 3.0 determines an explicit formula, is analyzed to …
A Stochastic Analog To The Richardson's Arms Race Model, John Fricks
A Stochastic Analog To The Richardson's Arms Race Model, John Fricks
Masters Theses & Specialist Projects
In this thesis, a stochastic version of the Richardson's arms race model is developed through the method of birth-death processes. The expected value of the model is explored and shown to be analogous to the original deterministic arms race model. The numerical method of randomization is then expanded and applied to the stochastic model. A comparison is then made between outcomes of the deterministic and stochastic models.