Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2007-03-16
Nonlinear Sciences
Adaptation and Self-Organizing Systems
16 pages, 12 figures
Scientific paper
Complex systems may often be characterized by their hierarchical dynamics. In this paper do we present a method and an operational algorithm that automatically infer this property in a broad range of systems; discrete stochastic processes. The main idea is to systematically explore the set of projections from the state space of a process to smaller state spaces, and to determine which of the projections that impose Markovian dynamics on the coarser level. These projections, which we call Markov projections, then constitute the hierarchical dynamics of the system. The algorithm operates on time series or other statistics, so a priori knowledge of the intrinsic workings of a system is not required in order to determine its hierarchical dynamics. We illustrate the method by applying it to two simple processes; a finite state automaton and an iterated map.
Görnerup Olof
Nilsson Jacobi Martin
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