Dynamically Generated Hierarchies in Games of Competition and the Role of Stochastic Fluctuations

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We shall consider cyclic games of competition with individuals occurring in N species, where each species is the prey of and preys on r smaller than N cyclically chosen other species. Predation here stands for one realization of suppression or competition. Aside from the interaction via predation or prey we consider reproduction, death, diffusion and mutation of individuals as basic processes on the scale of the underlying grid. In our intended collaboration we want to address the following questions: 1. For which combination of numbers r and N and for which choice of rates do we observe coexisting games on different scales like a fractal of rock-paper-scissor games, or the formation of larger, mutually competing domains, where the players inside a domain keep on playing another kind of game? 2. What is a suitable framework to derive the hierarchies of games on different spatial scales which we currently observe in our Gillespie simulations? 3. What is the impact of the different origins of stochastic fluctuations, how does their relative strength scale in terms of the system size? 4. What kind of aging processes are observed in these systems? Due to the inherent, dynamically generated multiple time scales and the competing interactions, we expect to observe effects, which satisfy the criteria of physical aging. Possible applications of our games range from microbial to ecological and social systems.