Complex systems of interest in contemporary science and technology can often be viewed as networks of interacting subsystems or subnetworks. In the simplest, and so far most studied cases, subnetworks all run on the same clock, are updated simultaneously, and dynamics is governed by a fixed set of dynamical equations. In biology, especially neuroscience, and technology, for example large distributed systems, these assumptions often do not hold: components may run on different clocks, there may be switching between between different sets of network dynamical equations and, most significantly, components of the network may run independently of the rest of the network for periods of time. We say networks of this type are asynchronous. The project will develop a theory of dynamics on adaptive asynchronous networks with a focus on finding conditions imply predictability and functionality of the network, notably the avoidance of deadlock and race conditions. Methods will use techniques from the statistical theory of dynamical systems, networks, and stochastic analysis as well as ideas coming from correlation based learning and computational neuroscience. Among many applications, we remark the potential for significantly improved understanding of large distributed networks (both technological and biological), as well as dynamical system based models for qualitative computing, learning and pattern recognition.
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