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We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and non-survivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterisation is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept -- the {\it dynamical fugacity}. Remarkably, in the large-mass limit, the survival probability of a node becomes independent of network geometry, and assumes a simple form which depends only on its mass and degree., Comment: 12 pages, 6 figures, 2 tables

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying NK landscapes with varying values of K., Comment: arXiv admin note: substantial text overlap with arXiv:0810.3492, arXiv:0810.3484