Here is some help regarding down loading maple 7 to a Mac and here is some help for loading it onto a PC .
Our first template can be used to solve a first order differential equation with one dependent and one independent variable. In this case we are solving
Here is an example were we explore some possible parameter changes when modeling fish populations.
Here is the Lokta-Volterra type model of our fish and fisher folk and here is the alligator model. Here are the three models for a "ecosystem" involving fish, alligators and fisher-folk that you developed in class JPAK , STA ,and AMRN .
dy/dt=-y+axy
Part of or motivation is as we vary the parameter a from 1.1 to 2 we see a bifurcation , in other words a qualitative change in the systems behavior. In order to understand this we zoom into the equilibrium and notice that near its equilibrium point the solution to this equation really does behave like those of the equation's linearization . Fortunately (up to to a wiggle) we can determine the qualitative properties of the solution from its linearization, and in this program we see how to take a system along with a known equilibrium point and find its linearization and explore this linear systems eigenvalues. Recall the linear system's eigenvalues allow us to determine the original system's qualitative properties near the equilibrium point by comparing it to a standard linear model.