# SageDynamics/Demo

This WorkingWiki page demonstrates the use of my Sage classes for high-level analysis of ODE dynamical systems.

On this page I construct a simple population biology model of two populations, and analyze and evaluate it.

This page uses Sage, Python, and makefile code stored on other pages:

Here is the source code for this page's demo: Loading WorkingWiki file "ode-system-demo.sage.step" dynamically. If it doesn't load, click to view the page statically.

Here's what that program prints out, in LaTeX format: Loading WorkingWiki file "ode-system-demo.sage.out.latexml.html" dynamically. If it doesn't load, click to view the page statically.

Here's the state space plot that the program creates, showing a representative trajectory of the model's dynamics, with flow vector field and zero-net-growth isoclines:

- Loading WorkingWiki file "ode-system-demo.png" dynamically. If it doesn't load, click to view the page statically.

And a bifurcation diagram of total population vs. ${\alpha}_{12}$ (black=stable, red=repelling point, blue=saddle):

- Loading WorkingWiki file "bifurcation-diagram.png" dynamically. If it doesn't load, click to view the page statically.