A neglected mathematical theory is enjoying new popularity, thanks to its relevance to network dynamics in biological systems. The beating of a leech's heart is just one example that has a mathematical basis in ‘groupoid theory’.
This is a preview of subscription content, access via your institution
Relevant articles
Open Access articles citing this article.
-
The discontinuum of river networks: the importance of geomorphic boundaries
Landscape Ecology Open Access 14 March 2023
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
References
Guelzim, N., Bottani, S., Bourgine, P. & Kepes, F. Nature Genet. 31, 60–63 (2002).
Solé, R. V. & Pastor-Sattaras, R. in Handbook of Graphs and Networks (eds Bornholdt, S. & Schuster, H. G.) 145–167 (Wiley-VCH, Berlin, 2003).
Grassberger, P. Math. Biosci. 63, 157–172 (1983).
Neutel, A.-M., Heesterbeek, J. A. P. & de Ruiter, P. C. Science 96, 1120–1123 (2002).
Golubitsky, M., Stewart, I., Collins, J. J. & Buono, P.-L. Nature 401, 693–695 (1999).
Bressloff, P. C., Cowan, J. D., Golubitsky, M., Thomas, P. J. & Wiener, M. C. Phil. Trans. R. Soc. Lond. B 356, 299–330 (2001).
Stewart, I. & Cohen, J. in Nonlinear Phenomena in Biological and Physical Sciences (eds Malik, S. K., Chandrasekharan, M. K. & Pradhan, N.) 1–63 (Indian Natl Sci. Acad., New Delhi, 2000).
Stewart, I., Elmhirst, T. & Cohen, J., in Bifurcations, Symmetry, and Patterns (eds Buescu, J., Castro, S. & Dias, A. P. S.) 3–54 (Birkhäuser, Basel, 2003).
Stewart, I. Phil. Trans. R. Soc. Lond. A 361, 1101–1123 (2003).
Mirollo, R. E. & Strogatz, S. H. SIAM J. Appl. Math. 50, 1645–1662 (1990).
Pecora, L. M. & Carroll, T. L. Phys. Rev. Lett. 64, 821–824 (1990).
Boccaletti, S., Pecora, L. M. & Pelaez, A. Phys. Rev E 63, 066219 (2001).
Wang, X. F. Int. J. Bifurc. Chaos 12, 885–916 (2002).
Stewart, I., Golubitsky, M. & Pivato, M. SIAM J. Appl. Dyn. Syst. (in the press).
Weinstein, A. Not. Am. Math. Soc. 43, 744–752 (1996).
Calabrese, R. L. & Peterson, E. Symp. Soc. Exp. Biol. 37, 195–221 (1983).
Gramoll, S., Schmidt, J. & Calabrese, R. L. J. Exp. Biol. 186, 157–171 (1994).
Golubitsky, M., Josic, K. & Kaper, T. J. in Global Analysis of Dynamical Systems (eds Broer, H., Krauskopf, B. & Vegter, C.) 277–308 (Inst. Phys., Bristol, 2001).
Milo, R. et al. Science 298, 824–827 (2002).
Shen-Orr, S., Milo, R., Shmoolik, M. & Alon, U. Nature Genet. 31, 64–68 (2002).
Tutte, W. T. Graph Theory (Addison-Wesley, Menlo Park, 1984).
Kauffman, S. A. J. Theor. Biol. 22, 437–467 (1969).
Wolfram, S. (ed.) Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).
Golubitsky, M. & Stewart, I. The Symmetry Perspective (Birkhäuser, Basel, 2002).
Grimmett, G. R. & Stirzaker, D. R. Probability and Random Processes (Clarendon, Oxford, 1992).
Barnsley, M. F. Fractals Everywhere (Academic, Boston, 1993).
Mainzer, K. Thinking in Complexity (Springer, Berlin, 1994).
Watts, D. J. & Strogatz, S. H. Nature 393, 440–442 (1998).
Newman, M. E. J. SIAM Rev. 45, 167–256 (2003).
Kuramoto, Y. Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
Burn, R. P. Groups: A Path to Geometry (Cambridge Univ. Press, 1985).
Brandt, H. Math. Ann. 96, 360–366 (1927).
Golubitsky, M., Nicol, M. & Stewart, I. Some Curious Phenomena in Coupled Cell Networks (in the press).
Singer, W. Neuron 24, 49–65 (1999).
Ashwin, P., Buescu, J. & Stewart, I. Nonlinearity 9, 703–737 (1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stewart, I. Networking opportunity. Nature 427, 601–604 (2004). https://doi.org/10.1038/427601a
Issue Date:
DOI: https://doi.org/10.1038/427601a
This article is cited by
-
The discontinuum of river networks: the importance of geomorphic boundaries
Landscape Ecology (2023)
-
Neural network equations and symbolic dynamics
International Journal of Machine Learning and Cybernetics (2015)