This thesis concerns itself with three different stochastic models: the selfdestructive percoaltion model, the invasion percolation model and a stochastic dynamic for the incipient infinite cluster model. These models are all defined on a graph in the plane denoted by Z, which is obtained by taking the points of R with integer coordinates as vertices and two vertices are connected with an edge ...

Aim Species' native ranges reflect the net outcome of interactions between life-history strategies and biotic and abiotic influences over evolutionary timescales. Differences in native ranges might be indicative both of relative historical performance, and adaptability to new conditions. Consequently, the native ranges of successful invaders might have distinctive biogeographical characteristic...

We have performed computer simulations of Kauffman’s automata on several graphs such as the regular square lattice and invasion percolation clusters in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent z) and propagation speeds of the damage when one adds a damaging agent, nicknamed ”strange man”. Despite the increase in the damaging effic...

We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of Ld−1 × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship betw...