At the start I was unsure what approach I should use to model this system, I considered using a discrete method such as with cellular automata but it just didn't feel right. I had already worked on modelling reaction-diffusion systems with coupled differential equations and so I thought I would stick with my strength.
I found a number of books rather useful:
- Complex population dynamics - Blasius, Kurths and Stone : ISBN-13: 978-9812771575
- Mathematical methods of population biology - Hoppensteadt : ISBN-13: 978-0521282567
- Pattern formation and dynamics in non-equilibrium systems - Cross and Greenside : ISBN-13: 978-0521770507
I coded the simulation of the system in FreeBaisc. The model itself is in 0 + 2 dimensions. I haven't analysed the 2D output screen capture yet although I have been analysing the phase portraits of specific spatial locations and also the stability analysis of the equations themselves. But in the interest of prettiness here is a picture of a 2D output (explanation to follow).
