Click a cell to make it into a barrier, where both populations are stuck at zero.

Adjust values below. Play around with the values and see what happens.

A: 5   B: 6   C: 6   D: 6
Each square is running a Lotka-Volterra predator/prey model but with the total number of predators and prey summed over all neighbouring squares.

More mathematically we can say that there are two populations, prey p and predators q. The change in the population of the i, j 'th square is given by the equations

change in p
change in q
Where P and Q are the sums of the populations of all the neigbouring squares. Or mathematically said:
def of P
def of Q

Please notice the asymmetry in the second equation: The rate at which the predators die in a square is not affected by the neighbouring squares. To keep the factors at the same size we have added a factor nine here (all other parts depend on the population in squares). Also notice that the model assumes that B (the rate at which the predators eat prey) and C (the rate at which predators die) are negative numbers. If you change them to positive ones, the populations will blow up.

The color goes from white (population exactly zero) to the darkest (population 1). The population itself can however increase above 1. Also note that as opposed to the normal Lotka-Volterra equations, here the population of a square can go to exactly zero, but not below that.