Fig. 7.

Number of prey, left, and predators, right, obtained from the deterministic model, equation (24), at the two boundaries, x = 0 and x = 20, as a function of time. The initial steep rise of the number of prey at x = 20 is due to the absence of predators in this region and cannot be fully seen here. It is followed by a sharp peak of predators. We see that during the first few oscillations the number of individuals can often be close to zero, indicating that extinction would be possible at those times in the corresponding stochastic model. At later times t > 20 the number of prey and predators is fluctuating with minima sufficiently away from zero, making extinction at those times less likely.