This system is inspired in the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. The dynamics of the process has two steps. In the growth step, each occupied site j dies but sends a Poisson[β] number of children to sites chosen uniformly at random from those at distance less than or equal to R from j. In the epidemic step, each site is hit by the epidemic with some small probability ε>0. If an occupied site j is hit, the epidemic spreads instantaneously to all the neighbors of j and so on, so all the connected component of occupied sites containing j is wiped out. For details see the paper.
Here is also a movie of the simulation run in a 2-dimensional torus (400x400), with β=2*log(3) and ε=0.01:
Short version (15 sec, 19.6 MB)
Long version (60 sec, 75.7 MB)
C source code: chaoticCP.tar.gz
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