This document contains the analysis of two biological systems modeled by differential equations. For the first system modeling insulin production, the author calculates the equilibrium points and determines the stability conditions to be β > (2α - 1)/(α - 1)2 for continual insulin production. For the second system modeling population dynamics, the author calculates the positive equilibrium point to be (1, r), determines stability for 0 < r < 2, and identifies a Hopf bifurcation occurring at r = 2 that generates periodic orbits, changing the stability properties.