Abstract
Asynchronous networks form a natural framework for many classes of dynamical networks encountered in technology, engineering and biology. Typically, nodes can evolve independently, be constrained, stop, and later restart, and interactions between components of the network may depend on time, state, and stochastic effects. We outline some of the main ideas, motivations and a basic result.
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For example, view Fig. 1 as being part of a threaded computer program and \(\mathbf {E}^a,\cdots ,\mathbf {E}^h\) as being synchronization events – evolution of associated threads is stopped until each thread has finished its computation; variables are then synchronized across the threads.
References
U. Alon, An Introduction to Systems Biology. Design Principles of Biological Circuits (Chapman & Hall/CRC, Boca Raton, 2007)
C. Bick, Local representation of asynchronous networks by Filippov systems (in preparation)
C. Bick, M.J. Field, Asynchronous networks and event driven dynamics (preprint)
C. Bick, M.J. Field, Asynchronous networks: modularization of dynamics theorem (preprint)
R. David, H. Alla, Discrete, Continuous, and Hybrid Petri Nets (Springer, Berlin, 2010)
F. Dörfler, M. Chertkov, F. Bullo, Synchronization in complex oscillator networks and smart grids. PNAS 110(6), 2005–2010 (2013)
A.F. Filippov, Differential Equations with Discontinuous Righthand Sides (Kluwer Academic Publishers, 1988)
W. Gerstner, R. Kempter, L.J. van Hemmen, H. Wagner, A neuronal learning rule for sub-millisecond temporal coding. Nature 383, 76–78 (1996)
N. Kashtan, U. Alon, Spontaneous evolution of modularity and network motifs. PNAS 102(39), 13773–13778 (2005)
J. Ladyman, J. Lambert, K. Wiesner, What is a complex system? Eur. J. Philos. Sci. 3(1), 33–67 (2013)
L.M. Pecora, T.L. Carroll, Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109–2112 (1998)
Acknowledgements
C. Bick is supported, in part, by NSF Grant DMS-1265253 and Marie Curie IEF Fellowship (project 626111). M.J. Field is supported, in part, by NSF Grant DMS-1265253 and Marie Curie IIF Fellowship (project 627590).
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Bick, C., Field, M.J. (2017). Asynchronous Networks. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_3
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DOI: https://doi.org/10.1007/978-3-319-55642-0_3
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