Figure 3. The suppression of global oscillations in the presence of quenched and annealed randomness of interaction graph (see legend), brought about by the sufficiently large fraction v of nodes that have a lower site-specific invasion rate w_j = 0.1 than the rest of the population at w_j = 1.

Presented results demonstrate that quenched site-specific invasion rates drawn from a simple discrete double-peaked distribution are apt to fully suppress global oscillations (note that the value of the order parameter A drops to zero at a sufficiently large value of v in both cases), regardless of the type of randomness in the interaction network that enables them. We have used Q = 0.5 for the fraction of rewired links determining the level of quenched randomness, and P = 0.5 as the probability for a potential target of an invasion to be selected randomly from the whole population rather than from nearest neighbors determining the level of annealed randomness of network.