Reaction-Diffusion Systems The Fight For Life

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Presentation transcript:

Reaction-Diffusion Systems The Fight For Life

Reaction-Diffusion Systems The Fight For Life

System of Equations Modeling Non-interacting Species

System of Equations for Interacting Species

Initial Conditions for our system Prey Predator

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

The Reaction-Diffusion System General Solutions for the system

Solving the system Step 1: Step 2:

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

Voila!

Voila!

Voila!

This leaves us with:

Matrix Equation and Eigenvalues

This system models many predator prey relationships