First, follow through the general theory of solving differential equations:
Some basic methods for solving a differential equation by computer.
then play with a simple Matlab code until you understand how it works:
A Matlab code to simulate a swinging pendulum. This code demonstrates a simple method for solving an ODE. Next, read through the general theory of modeling diffusion:
Explains how we model diffusion and its connection to diffusion equations and run + alter the relevant Matlab code below, again making sure you understand how it works.
Matlab code to simulate basic diffusion.
For the challenge, you will select one of the following three projects, each of which combine spatial diffusion with a system that can produce oscillations.
The goal is to generate a system where, without spatial variation all species die out, but with spatial heterogeneity, such as a random spatial distribution for initial conditions, diffusion in space allows both species to survive. Once you achieve this, (or if necessary without achieving this) you can study spatial patterns or adapt and improve the model.
Read the description of the model
The goal is to to study traveling waves in space, and produce spiral waves under conditions where without spatial variation, the steady state solution is flatline.
The goal is to to study traveling waves in space, and produce spiral waves under conditions where without spatial variation, the steady state solution is flatline. Since I was unable to achieve this in this system, glory to anyone who produces a stable spiral wave under any conditions. You may want to analyze parameters that affect the wavelength and period of oscillations.