Scholarpedia: Encyclopedia of Dynamical Systems

By Eugene Izhikevich

Encyclopedia of Dynamical Systems

Editor-in-Chief: Eugene M. Izhikevich, Ph.D., Mathematics

Members of SIAM are invited to participate in the Encyclopedia of Dynamical Systems, which is hosted by Scholarpedia --- the free peer-reviewed encyclopedia that anybody can edit. This project combines the philosophies of Encyclopedia Britannica and Wikipedia. Articles are written by leading experts in the field (invited by the editor-in-chief or elected by the public) and peer reviewed. Upon acceptance, the author becomes the article's curator. In contrast to Wikipedia, any future modification of an article in Scholarpedia must be approved by its curator before it appears online.

Among participants of this project are D. Anosov (Anosov Diffeomorphism), L. Bunimovich (Dynamical Billiards), N. Fenichel (Normal Hyperbolicity), R. FitzHugh (FitzHugh-Nagumo Model), J. Guckenheimer (five articles on codimension-two local bifurcations), M.W. Hirsch (Monotone Dynamics), P. Holmes (Stability, with Shea-Brown), A. Katok (Ergodic Theory and Invariant Measure), Y. Kuramoto (Kuramoto Model), Yu.A. Kuznetsov (seven articles on local bifurcations), E.N. Lorenz (Butterfly Effect), B. Mandelbrot (Fractals and Mandelbrot Set), J. Milnor (Attractor), E. Ott (Controlling Chaos, Crises, Boundary of Attraction, Attractor Dimensions), O. Rössler (Rössler Attractor), A.N. Sharkovsky (Sharkovsky Ordering), A. Shilnikov (Shilnikov Bifurcation), Y. Sinai (SRB Measure and Kolmogorov-Sinai Entropy), S. Smale (Morse-Smale Systems, with Shub and Palis), and many others.

Approximately 80% of topics in the Encyclopedia of Dynamical Systems have been already reserved. Available topics are depicted in black. If there are missing topics, please add them to the list (you need to be registered to do that; see below). If you would like to contribute an article, email your proposal to the Editor-in-Chief. Typically, authors of Scholarpedia have a PhD or MD and a tenured/tenure-track or equivalent position.

The Encyclopedia of Dynamical Systems, upon completion, will be published in a printed form. However, the main purpose of the encyclopedia is to remain freely available on the web, so that articles could be regularly updated and cross-referenced. If there is enough interest in the community for this project, the Encyclopedia of Dynamical Systems will be used as a seed to start an Encyclopedia of Applied Mathematics, and later an Encyclopedia of Mathematics.

Scholarpedia will also host lecture notes of semester-long courses on dynamical systems and related topics. The idea is to use the wiki-style mechanism built-in in Scholarpedia to evolve the lecture notes to a high-quality series of courses, which will be freely available online and could be used in many universities as standard teaching material on dynamical systems. Please, send your proposals to the Editor-in-Chief.

Current status of Scholarpedia:

Number of registered users: 1073
Number of registered curators: 411
Highest Scholar Index: 36 (Ed Ott and Jeff Moehlis)
Number of reserved articles: 464 (by curators)
Number of finished articles: 84
Number of peer-reviewed and accepted articles: 46
see also the list of contents
Most cited article (75 links): Meiss J. (2007) Dynamical Systems. Scholarpedia.
Number of articles with ongoing election of authors: 62

Some recent articles:

Milnor J.W. (2006) Attractor. Scholarpedia, p.4862
Sanders J.A. (2006) Averaging. Scholarpedia, p.5464
Murdock J. (2006) Unfoldings. Scholarpedia, p.6034
Murdock J. (2006) Normal Forms. Scholarpedia, p.4523
Carr J. (2006) Center Manifold. Scholarpedia, p.6370
Kuznetsov Yu. (2006) Andronov-Hopf Bifurcation. Scholarpedia, p.3799
Kuznetsov Yu. (2006) Saddle-Node Bifurcation. Scholarpedia, p.3778
Canavier C.C. (2006) Phase Response Curve. Scholarpedia, p.6796
Letellier C. and Rössler O.E. (2006) Rössler Attractor. Scholarpedia, p.3805
Sauer T.D. (2006) Attractor Reconstruction. Scholarpedia, p.2769
Ermentrout G.B. (2007) XPPAUT. Scholarpedia, p.4655

There is an ongoing election of authors for such topics as Bifurcation, Relaxation Oscillator, Chaos, Resonance, and many others.

Please, register with the invítation key 'siam' and participate in the election of authors. Self-nominations are welcome. Registration will also allow you to add topics to the encyclopedia.

Eugene M. Izhikevich
The Neurosciences Institute, San Diego, California.

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