|||R. E. Mirollo and S. H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM Journal on Applied Mathematics, 50(6):1645-1662, Dec. 1990. [ bib ]|
|||P. M. Narins. Frog communication. Scientific American, 273:78-83, Aug. 1995. [ bib ]|
|||P. M. Narins. Wie Frösche einander übertönen. Spektrum der Wissenschaft, pages 90-95, Nov. 1995. [ bib ]|
M. E. J. Newman.
Random graphs as models of networks.
In S. Bornholdt and H. G. Schuster, editors, Handbook of Graphs
and Networks. Wiley-VCH, Berlin, 2002.
[ bib |
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks such as the Internet, social networks or biological networks it leaves a lot to be desired. In particular, it differs from real networks in two crucial ways: it lacks network clustering or transitivity, and it has an unrealistic Poissonian degree distribution. In this paper we review some recent work on generalizations of the random graph aimed at correcting these shortcomings. We describe generalized random graph models of both directed and undirected networks that incorporate arbitrary non-Poisson degree distributions, and extensions of these models that incorporate clustering too. We also describe two recent applications of random graph models to the problems of network robustness and of epidemics spreading on contact networks.
R. A. Oliva and S. H. Strogatz.
Dynamics of a large array of globally coupled lasers with distributed
International Journal of Bifurcation and Chaos,
11(9):2359-2374, Sept. 2001.
[ bib ]
We analyze a mean-field model for a large array of coupled solid-state lasers with randomly distributed natural frequencies. Using techniques developed previously for coupled nonlinear oscillators, we derive exact formulas for the stability boundaries of the phase locked, incoherent, and off states, as functions of the coupling and pump strength and the spread of natural frequencies. For parameters in the intermediate regime between total incoherence and perfect phase locking, numerical simulations reveal a variety of unsteady collective states in which all the lasers' intensities vary periodically, quasiperiodically, or chaotically.
|||C. Pöppe. Ein mathematisches Modell für das Liebeswerben der Glühwürmchen. Spektrum der Wissenschaft, pages 18-19, May 1992. [ bib ]|
|||S. H. Strogatz. Love affairs and differential equations. Mathematics Magazine, 61(1):35, Feb. 1988. [ bib ]|
|||S. H. Strogatz. Exploring complex networks. Nature, 410:268-276, 8 March 2001. [ bib ]|
|||S. H. Strogatz and I. Stewart. Coupled oscillators and biological synchronization. Scientific American, 269:102-109, Dec. 1993. [ bib ]|
|||S. H. Strogatz and I. Stewart. Gekoppelte Oszillatoren und biologische Synchronisation. Spektrum der Wissenschaft, pages 74-81, Feb. 1994. [ bib ]|
|||D. J. Watts and S. H. Strogatz. Collective dynamics of 'small-world' networks. Nature, 393:440-442, 4 June 1998. [ bib ]|
This file was generated by bibtex2html 1.96.