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- Duncan J. Watts, Steven H. Strogatz
- Nature
- 1998

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological,… (More)

- M. E. J. Newman, Steven H. Strogatz, Duncan J. Watts
- Physical review. E, Statistical, nonlinear, and…
- 2001

Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition… (More)

- R. Mirollo, Steven H. Strogatz, RENATO E. MIROLLOt, Steven H. Strogatz
- 1990

A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker [Mathematical aspects of heartphysiology, Courant Institute of Mathematical Sciences, New York University, New York, 1975, pp. 268-2781 is studied. The model consists of a population of identical integrate-and-fire oscillators. The coupling… (More)

- Steven H. Strogatz
- Nature
- 2001

The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear… (More)

A tabletop waterwheel, designed and built by Prof. Willem Malkus (Math. Dept., MIT), is used to demonstrate chaos in a mechanical analog of the Lorenz equations. The waterwheel’s rotational damping rate can be adjusted by tightening or loosening a brake. When the brake is not too tight, the wheel settles into a steady rotation. Either direction of rotation… (More)

The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain threshold, the system exhibits a phase transition: some of the oscillators spontaneously synchronize, while others remain incoherent. The mathematical analysis of… (More)

- Duncan Callaway, M. E. J. Newman, Steven H. Strogatz, Duncan J. Watts
- Physical review letters
- 2000

Recent work on the Internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes or links. Such deletions include, for example, the failure of Internet routers or power transmission lines. Percolation models on random graphs provide a simple representation of this process… (More)

- M. E. J. Newman, Duncan J. Watts, Steven H. Strogatz
- Proceedings of the National Academy of Sciences…
- 2002

We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of real-world… (More)

- Jordi García-Ojalvo, Michael B. Elowitz, Steven H. Strogatz
- Proceedings of the National Academy of Sciences…
- 2004

Diverse biochemical rhythms are generated by thousands of cellular oscillators that somehow manage to operate synchronously. In fields ranging from circadian biology to endocrinology, it remains an exciting challenge to understand how collective rhythms emerge in multicellular structures. Using mathematical and computational modeling, we study the effect of… (More)

SFI WORKING PAPER: 2000-07-042 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty,… (More)