1. Reaction-Diffusion Systems The Fight For Life

2. Reaction-Diffusion Systems The Fight For Life

3. System of Equations Modeling Non-interacting Species

4. System of Equations for Interacting Species

5. Initial Conditions for our system
Prey
Predator

6. We begin solving our system like a heat equation with a source term
Heat Equation with a source term and insulated boundaries

7. The Reaction-Diffusion System
General Solutions for the system

8. Solving the system
Step 1:
Step 2:

9. And with these magic substitutions…
Continuing to solve…
And with these magic substitutions…
A System of ODE’s:

10. Voila!

11. Voila!

12. Voila!

13. This leaves us with:

14. Matrix Equation and Eigenvalues

15. This system models many predator prey relationships